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2020-04-11, 18:53
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#12 |
Dec 2008
you know...around...
2·11·29 Posts |
Called out in the dark
(I always cringe a little when I see my hastily written post # 8 above with "q=2p", where I meant to say that q equals twice a prime number; might as well have written "q: prime"...)
Well, here's the data as of 2020-04-09. q=934 was a close one in terms of CSG value. Code:
q: common difference in arithmetic progression p+k*q CSG: Cramér-Shanks-Granville ratio via gap/phi(q)/log(p')² where p'=p+gap CSG_max: maximum value found for CSG up to p_limit p: initial prime of the gap p_limit: search limit for p' q CSG_max gap p p_limit 2 0.7394648022 210 20831323 3600000000 4 0.7678340865 684 1464395089 7200000000 6 0.7541322181 462 39895309 10800000000 8 0.7436946715 1424 3176384429 14400000000 10 0.8043339165 1610 5189671259 18000000000 12 0.8052809769 1740 12411153017 21600000000 14 0.8096072055 2310 2955286913 25200000000 16 0.9046153418 3728 7194688583 28800000000 18 0.7887450235 702 194027 32400000000 20 0.7944296249 1600 7775737 36000000000 22 0.8617839921 2002 4160719 39600000000 24 0.7948892517 3720 31920285041 43200000000 26 0.7982175172 5694 38786373547 46800000000 28 0.8452080697 3836 279251711 50400000000 30 0.8058232068 1980 40846943 54000000000 32 0.8965150715 3808 11911369 57600000000 34 0.8182937153 3876 29673503 61200000000 36 0.7872577337 5400 24166901071 64800000000 38 0.8518980455 2280 195271 68400000000 40 0.8172390325 6360 3785091139 72000000000 42 0.8251402679 3780 305816297 75600000000 44 0.7778447835 1980 77369 79200000000 46 0.8034522392 7268 640376543 82800000000 48 0.7973452005 7344 26302298977 86400000000 50 0.8793539278 4950 19315399 90000000000 52 0.7726636783 7332 432150907 93600000000 54 0.7956494153 7344 6831679457 97200000000 56 0.7926567144 5376 19980397 100800000000 58 0.7831435896 8932 582284587 104400000000 60 0.7533972457 6180 6814968631 108000000000 62 0.7480209472 13392 40678798409 111600000000 64 0.8613806693 7104 9370547 115200000000 66 0.7637963086 9834 104493100477 118800000000 68 0.7981407159 13056 6594265703 122400000000 70 0.8282785007 11900 42252957959 126000000000 72 0.8602785358 4824 4344187 129600000000 74 0.9131005021 9620 26876579 133200000000 76 0.8416067457 16796 16804480523 136800000000 78 0.7510340136 9828 13836158729 140400000000 80 0.7585177824 10720 1339392487 144000000000 82 0.8163798773 2214 1553 147600000000 84 0.8017445129 11172 29153099231 151200000000 86 0.8236614027 9718 19002559 154800000000 88 0.8074176319 3344 22907 158400000000 90 0.7952351245 8460 1391789947 162000000000 92 0.8569074437 19320 6775293947 165600000000 94 0.7540215308 21244 55988532973 169200000000 96 0.7835562193 6816 14461861 172800000000 98 0.8195247347 12936 262621343 176400000000 100 0.7274868378 15500 10549382033 180000000000 102 0.7887967496 16626 139972076507 183600000000 104 0.7885883689 24648 120860909123 187200000000 106 0.7406871356 15900 666737879 190800000000 108 0.8456207760 20196 153489937273 194400000000 110 0.7577236448 8250 14618897 198000000000 112 0.8754122474 19376 2117717087 201600000000 114 0.7615636029 9348 104547589 205200000000 116 0.7729502356 26796 63916863757 208800000000 118 0.8167041620 20886 1316371417 212400000000 120 0.8057216311 14040 13628678729 216000000000 122 0.7947909820 28182 36113593211 219600000000 124 0.8316652784 30628 57483096991 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0.7536441567 13230 202008439 378000000000 212 0.8726800198 57028 76983450889 381600000000 214 0.8300985533 54570 65376711233 385200000000 216 0.8565309700 38016 60639375773 388800000000 218 0.8000713650 60386 302626514693 392400000000 220 0.8516677011 11220 363019 396000000000 222 0.7476242389 35964 168120545239 399600000000 224 0.7530876774 27552 300702751 403200000000 226 0.8205657931 65314 378168298933 406800000000 228 0.7687388396 35568 102156515693 410400000000 230 0.8278708905 49910 232943726651 414000000000 232 0.7860150605 25288 22918543 417600000000 234 0.7932876948 27144 2934877793 421200000000 236 0.8808741581 53100 7947586583 377600000000 238 0.7961571214 47838 73308073691 380800000000 240 0.7746515981 25440 6883929373 384000000000 242 0.8312839360 32912 173468021 387200000000 244 0.8153157728 64172 132595555181 390400000000 246 0.8801251829 47478 189457586089 393600000000 248 0.8449133277 22816 3249793 396800000000 250 0.9603210373 53000 15946776179 400000000000 252 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68522931313 478800000000 800 0.7854380237 124000 4429597201 480000000000 802 0.8127895345 231778 394291297993 481200000000 804 0.7850960183 134268 113158700561 482400000000 806 0.9079408402 82212 7638601 483600000000 808 0.7877421483 113120 169209149 484800000000 810 0.8116850129 89910 6836640043 486000000000 812 0.8851736046 157528 9883553821 487200000000 814 0.7938088485 104192 196064567 488400000000 816 0.8066643398 61200 29890303 489600000000 818 0.8335856530 112884 81576293 490800000000 820 0.8731640737 90200 63450923 492000000000 822 0.8762643516 110970 2349421741 493200000000 824 0.8675619063 149144 821531663 494400000000 826 0.7608164263 191632 482975333977 495600000000 828 0.7652805026 90252 1510362617 496800000000 830 0.9773893526 154380 3391062847 498000000000 832 0.8327364626 114816 169459867 499200000000 834 0.8070598355 81732 208384291 500400000000 836 0.7538505214 174724 104621735923 334400000000 838 0.8485627499 66202 791251 335200000000 840 0.8015664476 73920 3295891901 336000000000 842 0.7876682549 71570 2370917 336800000000 844 0.8376720882 181460 7295944001 337600000000 846 0.8142049032 83754 242174417 338400000000 848 0.8232748309 191648 18770276141 339200000000 850 0.9701528945 68850 2865899 340000000000 852 0.8246959945 74976 66856927 340800000000 854 0.7816720250 118706 831340553 341600000000 856 0.7892210034 221704 150881417317 342400000000 858 0.7730683037 55770 33794983 343200000000 860 0.7875830400 184040 283849393787 344000000000 862 0.7629563985 160332 3988841561 344800000000 864 0.8914155653 49248 986113 345600000000 866 0.7871098852 122972 181431827 346400000000 868 0.7913892342 123256 1079341177 347200000000 870 0.8374583079 82650 1305824189 348000000000 872 0.7561328839 190968 31683162491 348800000000 874 0.7722875504 180044 34472439539 349600000000 876 0.8255392548 135780 23908792657 350400000000 878 0.8059992615 178234 5732050237 351200000000 880 0.8181553201 134640 7058010781 352000000000 882 0.8094486988 98784 3607715213 352800000000 884 0.7567896075 177684 54800797889 353600000000 886 0.8355161599 239220 113074220731 354400000000 888 0.8258816962 101232 911045519 355200000000 890 0.8369225223 100570 105642601 356000000000 892 0.7741629232 202484 34734355067 356800000000 894 0.8349591749 82248 83596313 357600000000 896 0.8173757133 190848 51175902559 358400000000 898 0.7948385029 204744 25932816499 359200000000 900 0.8072861180 135000 290994718649 360000000000 902 0.8232989477 217382 143887883981 360800000000 904 0.7813795699 218768 71929518179 361600000000 906 0.8341247493 126840 5993514403 362400000000 908 0.8038721784 124396 108448177 363200000000 910 0.8725257404 66430 11447977 364000000000 912 0.7384255018 134064 80190699493 364800000000 914 0.7934699183 232156 100197840751 365600000000 916 0.8514071759 204268 9155647951 366400000000 918 0.8050224606 136782 35374365181 367200000000 920 0.8424586115 61640 1763849 368000000000 922 0.7601528076 214826 58158071267 368800000000 924 0.8530073203 69300 97746161 369600000000 926 0.8116795701 221314 35526795583 370400000000 928 0.8150834574 208800 24269915627 371200000000 930 0.9064778846 68820 52930403 372000000000 932 0.8943236869 212496 6725412643 372800000000 934 0.9991973371 137298 28542649 373600000000 * largest CSG value so far 936 0.8676912530 71136 21181103 374400000000 938 0.8053687523 217616 221046403007 375200000000 940 0.8089099343 177660 40714396309 376000000000 942 0.8067961396 87606 126384917 376800000000 944 0.8331691839 189744 4182919339 377600000000 946 0.7755322031 197714 50103406523 378400000000 948 0.7864516026 169692 263594116631 379200000000 950 0.8545569452 122550 465470219 380000000000 952 0.8405042747 119952 235628287 380800000000 954 0.8998573515 60102 2200661 381600000000 956 0.7626024207 247604 220062550277 382400000000 958 0.8529434109 214592 9196163681 383200000000 960 0.8904686989 120960 10093588667 384000000000 962 0.8144970096 88504 7634353 384800000000 964 0.8004216214 107004 17584639 385600000000 966 0.8283176903 122682 19348856179 386400000000 968 0.9204665049 279752 259460206361 387200000000 970 0.8013154534 204670 158734118899 388000000000 972 0.8225551898 150660 21178988759 388800000000 974 0.7782865462 219150 28420213067 389600000000 976 0.9105943329 278160 90346489859 390400000000 978 0.7903996503 165282 107942471909 391200000000 980 0.7846347168 117600 1487302123 392000000000 982 0.8063698833 262194 153969081667 392800000000 984 0.7799444190 169248 203888107831 393600000000 986 0.7924196264 225794 89694739373 394400000000 988 0.8062837244 204516 33384442471 395200000000 990 0.7913342257 97020 6544493717 396000000000 992 0.8327256129 248000 65733837647 396800000000 994 0.8168423482 217686 87037919861 397600000000 996 0.8046526420 66732 7982237 398400000000 998 0.8287134801 212574 7185918043 399200000000 1000 0.8366128339 192000 25270575311 400000000000 I gave my workplace PC a well deserved rest over Easter. Calculations will continue on Wednesday. |
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2020-04-12, 20:23
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#13 |
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Dec 2008
you know...around...
2×11×29 Posts |
 I notice that my code is well received, so I had to rewrite it a little and remove a bug that could give incorrect results (if any) when the starting point ps was less than d&. Attached is the new VBA code. |
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2020-04-30, 15:07
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#14 |
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Dec 2008
you know...around...
2×11×29 Posts |
Let's go Turbo!
(Are any fans of Beyblade around here?)
While moving in the 12-digit range, I noticed how inefficient my program is. I sieve the same numbers over and over again for every q. Quick-and-dirty analysis: each q sieves about 0.81 times (i.e. 8/pi²) the amount of numbers as the "base" interval (at q=2) while practically searching the same range for p. The thought of re-writing my program did hang around in my head for some time, but only recently I found out how urgent it is, and it took a whole weekend to come up with a satisfying solution that worked properly. All q <= 1000 are now searched up to p=8*1011, progressing at a speed of about 4.8*109 per hour, and another instance running in parallel searches 1000 < q <= 2690, currently at p=7.3*1010, and a throughput of about 2.3*109 per hour. I also have a plan in mind to take all q <= 30030 up to at least 1010, but I have yet to test if it works. Code:
q: common difference in arithmetic progression p+k*q CSG: Cramér-Shanks-Granville ratio via gap/phi(q)/log(p+gap)² CSG_max: maximum value found for CSG up to p=8*10^11 p: prime preceding the gap current record for CSG_max: 0.9991973371 @ q=934 q CSG_max gap p 2 0.7953486740 456 25056082087 4 0.8056652398 1044 113391385573 6 0.7541322181 462 39895309 8 0.7875867918 2080 144309631099 10 0.8930327253 2450 236455710509 12 0.8455173596 2352 283661812859 14 0.8345982115 2884 26448217657 16 0.9046153418 3728 7194688583 18 0.7887450235 702 194027 20 0.7944296249 1600 7775737 22 0.8617839921 2002 4160719 24 0.8117145259 4392 197036728351 26 0.8652413900 7540 505084610521 28 0.8452080697 3836 279251711 30 0.8058232068 1980 40846943 32 0.8965150715 3808 11911369 34 0.8182937153 3876 29673503 36 0.7872577337 5400 24166901071 38 0.8518980455 2280 195271 40 0.8172390325 6360 3785091139 42 0.8251402679 3780 305816297 44 0.8085714112 11132 248049290057 46 0.8034522392 7268 640376543 48 0.7973452005 7344 26302298977 50 0.8793539278 4950 19315399 52 0.7811165997 13832 626287370141 54 0.7956494153 7344 6831679457 56 0.8531838024 13272 113946560627 58 0.8160213701 17052 731647597039 60 0.7594431944 8760 457941678127 62 0.7505368847 16740 694602632629 64 0.8613806693 7104 9370547 66 0.7637963086 9834 104493100477 68 0.7981407159 13056 6594265703 70 0.8282785007 11900 42252957959 72 0.8602785358 4824 4344187 74 0.9131005021 9620 26876579 76 0.8416067457 16796 16804480523 78 0.7510340136 9828 13836158729 80 0.8244076217 19680 727457191561 82 0.8163798773 2214 1553 84 0.8017445129 11172 29153099231 86 0.8236614027 9718 19002559 88 0.8173745127 22528 251192223571 90 0.7952351245 8460 1391789947 92 0.8569074437 19320 6775293947 94 0.7540215308 21244 55988532973 96 0.7963941131 17280 203618303897 98 0.8195247347 12936 262621343 100 0.7442402852 20600 265671964073 102 0.7887967496 16626 139972076507 104 0.9499776231 31200 229169128997 106 0.9015411061 33072 342820240309 108 0.8456207760 20196 153489937273 110 0.7957899312 21780 229165433009 112 0.8754122474 19376 2117717087 114 0.8493019884 22116 478998886567 116 0.7977964383 32248 465563693299 118 0.8167041620 20886 1316371417 120 0.8057216311 14040 13628678729 122 0.7947909820 28182 36113593211 124 0.8316652784 30628 57483096991 126 0.9142860299 18270 17061510127 128 0.8323761564 7296 113623 130 0.7938556043 21450 20138027813 132 0.7846464407 10560 92494289 134 0.8397671201 14740 12075073 136 0.7672983613 26928 14785702759 138 0.7924769327 15042 1047660137 140 0.9112585981 31360 425297500759 142 0.8610872285 43026 401037154541 144 0.7893617069 17856 2678906773 146 0.8196507109 23652 494696261 148 0.7830010017 42328 794519516383 150 0.7557605255 21000 279561600257 152 0.7675315249 38456 286089015071 154 0.9369830338 35728 88779374809 156 0.7985008265 13728 165640219 158 0.7606501324 43134 512782039607 160 0.8211887580 36960 328840371359 162 0.8258805846 26244 34294519837 164 0.7924402630 47232 714913847737 166 0.8175587888 42828 94831438649 168 0.7739486136 24864 171996125029 170 0.7905258192 29240 27579604799 172 0.8745407940 38356 8387732083 174 0.8966388328 14616 25666717 176 0.8893387228 32912 2191630061 178 0.7718247316 44856 144798233893 180 0.7968104593 22680 37641351263 182 0.8820202987 27482 1082590961 184 0.8892744577 56856 508307558683 186 0.8021152848 15624 66824477 188 0.7964246226 40044 14217429113 190 0.8735201597 38950 64231886011 192 0.8583746127 11904 2459623 194 0.8234255916 44232 18757576997 196 0.8703957715 44100 46355125469 198 0.7511941018 20196 1560142237 200 0.8255106246 39800 45870059471 202 0.8455991259 26462 48134069 204 0.8383878988 31212 29818321129 206 0.8849004882 20806 3903223 208 0.8637254761 47008 21908990083 210 0.7941670680 27510 464338653979 212 0.8726800198 57028 76983450889 214 0.8300985533 54570 65376711233 216 0.8565309700 38016 60639375773 218 0.8025184444 64746 741341656273 220 0.8516677011 11220 363019 222 0.7476242389 35964 168120545239 224 0.7530876774 27552 300702751 226 0.8205657931 65314 378168298933 228 0.7687388396 35568 102156515693 230 0.8278708905 49910 232943726651 232 0.7860150605 25288 22918543 234 0.7932876948 27144 2934877793 236 0.9437796854 79296 487692833143 238 0.7961571214 47838 73308073691 240 0.8040958748 37680 564376543243 242 0.8312839360 32912 173468021 244 0.8153157728 64172 132595555181 246 0.8801251829 47478 189457586089 248 0.8449133277 22816 3249793 250 0.9603210373 53000 15946776179 252 0.8886298435 37800 35983220659 254 0.7778963787 45974 2545430123 256 0.7680769257 53248 12798115129 258 0.7684771240 45150 305996132599 260 0.7724350668 30160 573522601 262 0.8145777421 79386 778033843151 264 0.8241313527 46200 313621476739 266 0.8801702481 39368 688831433 268 0.7914716927 71020 210484888321 270 0.9385992389 27000 479487689 272 0.7985388488 59568 30497191399 274 0.9241529945 68500 13766905759 276 0.8452548271 33672 1738757609 278 0.8930499724 25854 1925299 280 0.7989596541 52360 222398285827 282 0.8508107698 23406 32332831 284 0.8785941526 66456 12436366727 286 0.7858974077 62920 165094766113 288 0.7935760257 50688 159328991309 290 0.7802020735 65250 737183466337 292 0.8835286349 35624 18463427 294 0.8874698444 31458 834434033 296 0.7407823594 59792 19144263221 298 0.8142218681 71520 38040537103 300 0.8694555188 31500 1746213839 302 0.7889783882 46206 381321631 304 0.9026153946 44688 112884059 306 0.8374812598 13464 403553 308 0.8043192128 57288 38073581723 310 0.8496494922 69750 228639573389 312 0.8318902760 51168 98393397133 314 0.8034115353 51810 676001831 316 0.7761217516 36024 30954479 318 0.8218376546 39114 1952210459 320 0.8298538635 68480 106433008811 322 0.8573533053 54740 3560039459 324 0.7994627901 61560 394806744763 326 0.8083900200 80848 61763668063 328 0.7963256514 70848 17418374759 330 0.7638121358 28380 2288156501 332 0.7948104095 73704 21234656767 334 0.7853352422 91850 337046857421 336 0.7538847566 48720 185386505651 338 0.8637454324 43602 64873867 340 0.8240596233 65280 63699574657 342 0.8010075672 59850 264946609777 344 0.9190160329 66736 1069426291 346 0.7997930054 84078 54543153053 348 0.8268505391 67512 532187265079 350 0.8106891221 61950 91077187501 352 0.7785409404 82720 155422575103 354 0.8053164792 59826 97833706423 356 0.8760991508 102172 151136306521 358 0.7782235660 36516 11215003 360 0.9190759335 23760 13367671 362 0.7574134126 91224 171412985833 364 0.7756310715 51324 2040279533 366 0.8000166747 25986 13943863 368 0.8051615730 105984 753348546229 370 0.7987557798 81400 357568042813 372 0.7936543460 69192 508077732887 374 0.8532053339 58344 951272459 376 0.8393024208 62040 506537617 378 0.7935133452 61236 406541144927 380 0.8062842535 70680 51924372169 382 0.7889373294 90916 49616984707 384 0.7939465677 43392 941956339 386 0.7891241447 86850 24998032091 388 0.8235266859 72556 2009863117 390 0.7826368919 45240 45380958619 392 0.8571708876 75656 9004407101 394 0.8099475511 32308 1536583 396 0.8578841605 68904 172082709217 398 0.8791459095 89152 6737268127 400 0.7989545605 12800 9371 402 0.7868411869 66732 101933130811 404 0.7941196209 83628 9237777071 406 0.8585658511 87696 51121166533 408 0.8204181763 66912 91749328751 410 0.7897091793 46740 225303313 412 0.8036159885 90228 15439142689 414 0.8961928199 80730 221437110397 416 0.8020117468 75296 4013157443 418 0.7948806774 102410 415898213609 420 0.7627980893 26880 209227433 422 0.8690265566 57814 53634703 424 0.7602757566 91584 28278509927 426 0.7914098117 71994 117628436659 428 0.8044283310 40660 5039641 430 0.8013985116 55470 653446711 432 0.8219377815 53568 1734713993 434 0.7722870211 104160 772698979163 436 0.8047788797 102896 36828863651 438 0.7961083251 57816 5663148871 440 0.8792757227 58520 720313157 442 0.7596162182 99450 219117304141 444 0.9438876646 15984 35257 446 0.7775995907 49060 20910913 448 0.7848311396 90944 46689332597 450 0.7619657101 57600 79481983369 452 0.7838385407 97632 17418654119 454 0.7682744177 118948 232873806283 456 0.8859311160 95304 741680341187 458 0.8209257626 71448 305532509 460 0.7705031462 72680 11329574903 462 0.8277181464 44814 1678178797 464 0.8354396498 55680 30933989 466 0.8675896733 26562 70937 468 0.8983741777 95940 671415930377 470 0.8680891345 94000 34320032563 472 0.8363640483 66080 103334411 474 0.8380885352 81528 69987740731 476 0.9122603335 97580 17812528859 478 0.8459786783 58316 24551903 480 0.8369451486 55200 7215375371 482 0.8084758201 85796 1355943101 484 0.7928372491 60984 131951387 486 0.9670602256 66582 897783067 488 0.8040919055 124928 112158744989 490 0.8378578846 82320 31813190909 492 0.7854804768 93480 699003369871 494 0.8392228848 79040 1171149593 496 0.7869001503 98704 8483101717 498 0.7903333451 86652 169488659107 500 0.7914911855 105000 153153439729 502 0.9346253968 41164 540139 504 0.8170280734 50400 974403323 506 0.8272732557 71852 425671457 508 0.8267616819 112776 12711671711 510 0.8611973391 44880 579426871 512 0.7850984980 121344 46897900787 514 0.9225813074 174246 625510735951 516 0.8019834578 72756 12362133493 518 0.8366088676 101010 18527678629 520 0.8696185442 109200 127816392311 522 0.7983405988 46458 120978283 524 0.8097368830 154580 586125879281 526 0.8115530554 94680 1460084749 528 0.8934942692 34848 5998913 530 0.8049360188 57240 107123117 532 0.7920246624 30324 575077 534 0.8161638595 88110 57019930549 536 0.7799025504 138288 179982795691 538 0.9016955220 112980 2457304483 540 0.8029054239 48060 715228027 542 0.8534940538 61246 11964913 544 0.8392434214 126208 33574445479 546 0.8836029793 94458 680726038129 548 0.8034500145 96996 1410813787 550 0.7885921427 109450 275839875067 552 0.7956321590 104880 768279045497 554 0.7914668223 147364 190546085857 556 0.8516820096 150676 98958026977 558 0.9544916211 106020 61428637987 560 0.7749958441 75040 5660034091 562 0.7812147343 151740 274490495683 564 0.8053315904 108852 589938736859 566 0.7891020079 127916 25853082041 568 0.8409819101 71568 37194763 570 0.8015346996 27930 5671207 572 0.7872642046 100100 9913066937 574 0.8355665622 104468 8173667093 576 0.7897361686 103680 227188645297 578 0.7884091107 106352 4694158901 580 0.8716154868 135720 282082451569 582 0.7329439961 103596 607263973321 584 0.7923222032 106872 2504438459 586 0.8159773780 133608 19239163373 588 0.7761971881 58212 1499370799 590 0.8344010904 123900 97104120731 592 0.9093598272 152736 30757758641 594 0.8203596194 103950 333275730829 596 0.8752581666 116220 1578834337 598 0.7933508876 113022 12263164867 600 0.7956697951 19200 196303 602 0.8671990408 55986 8882693 604 0.8070806533 103284 932676103 606 0.7796492138 96960 67559839063 608 0.8125159769 141664 48492135667 610 0.8365143363 40260 1372451 612 0.7978540809 44064 23167169 614 0.8275383515 68768 14281613 616 0.7562342777 116424 99877977587 618 0.8265107359 111240 142939098451 620 0.7625254531 44640 6020933 622 0.8063729000 93300 245534483 624 0.9394014419 132288 577632351979 626 0.8003908014 170898 229723986623 628 0.8690691013 152604 20089808047 630 0.7878195018 83790 635068094299 632 0.8457792089 182648 266552475209 634 0.8321349317 178154 201487337099 636 0.8465112163 94128 11000930573 638 0.7538727012 93148 1327646743 640 0.9120077454 55040 4602251 642 0.8152602768 77040 1475945477 644 0.8303242949 97244 1403478863 646 0.9148101139 191862 524463691699 648 0.8487263784 57024 45602917 650 0.7783532479 57850 43857397 652 0.8380466032 132356 3876681503 654 0.9214740453 51666 9881863 656 0.8450147043 194832 454517973809 658 0.8049383681 151998 228935733461 660 0.8043599214 95700 696335516473 662 0.7767298220 179402 308765222369 664 0.8497732615 179944 108343097587 666 0.9612073070 137196 145879569457 668 0.8291122833 161656 33463509787 670 0.8588802430 146730 111632773561 672 0.8377544361 92064 24553355279 674 0.8927385746 154346 7102999643 676 0.7911246648 81120 74589533 678 0.8188167676 101700 16846380763 680 0.7847062189 129880 110374441477 682 0.8756801286 157542 43180032209 684 0.8371047755 63612 139850671 686 0.8425141547 118678 3207660733 688 0.7914089252 87376 74464177 690 0.8298009290 93150 92923597009 692 0.8099695701 189608 213400291319 694 0.9352046150 222080 238517976413 696 0.8663493208 64728 85359893 698 0.7930566851 198930 456923141659 700 0.8284455357 136500 239460526523 702 0.7511986045 32292 1306499 704 0.8202954082 187264 397943965597 706 0.8695438095 40242 55201 708 0.8977861205 144432 273087013487 710 0.7724598204 149810 269015016161 712 0.8199108541 213600 652989609751 714 0.7953230813 113526 694348824997 716 0.7831859227 193320 272750735171 718 0.7661030339 186680 214029806201 720 0.8760847971 119520 377221918061 722 0.7617166259 131404 5674164913 724 0.7975329263 110772 339112381 726 0.8799338964 137940 391674855421 728 0.9518517909 184184 180789356273 730 0.8169767948 59130 7609781 732 0.8289374951 34404 479797 734 0.8603414239 198180 78573408271 736 0.7940567828 36064 49669 738 0.8187851952 69372 144447397 740 0.8024558855 102120 1346388959 742 0.8270690786 48972 912367 744 0.7697508611 124992 197934069341 746 0.8040409658 181278 49168511023 748 0.7830564314 139128 17115875771 750 0.8359892306 106500 91377216071 752 0.7749013078 128592 1668673339 754 0.7782240049 183222 313412732261 756 0.7984514297 71820 728533909 758 0.8307863368 161454 7035777923 760 0.8587348951 151240 54915038317 762 0.7947601914 132588 149362737379 764 0.8072228398 182596 39444378481 766 0.8360220240 124092 363645049 768 0.8159361794 104448 5146249133 770 0.8512445396 80850 435991117 772 0.7934001992 214616 336250303541 774 0.7963577306 77400 338022701 776 0.8694867562 95448 21931331 778 0.7896427008 161046 9056973697 780 0.7773942238 109200 558379404841 782 0.7925574832 168912 48563547259 784 0.8187678710 40768 152791 786 0.7375163313 128904 182041921063 788 0.8598576323 115836 112344431 790 0.7449992657 116130 5097460699 792 0.7809066212 131472 318121728761 794 0.8737191630 146096 839726627 796 0.8171350137 216512 171358508429 798 0.8189774650 110124 68522931313 800 0.7854380237 124000 4429597201 802 0.8127895345 231778 394291297993 804 0.7850960183 134268 113158700561 806 0.9079408402 82212 7638601 808 0.7877421483 113120 169209149 810 0.8116850129 89910 6836640043 812 0.8851736046 157528 9883553821 814 0.7938088485 104192 196064567 816 0.8066643398 61200 29890303 818 0.8335856530 112884 81576293 820 0.8731640737 90200 63450923 822 0.8762643516 110970 2349421741 824 0.8675619063 149144 821531663 826 0.7608164263 191632 482975333977 828 0.7652805026 90252 1510362617 830 0.9773893526 154380 3391062847 832 0.8327364626 114816 169459867 834 0.8070598355 81732 208384291 836 0.7538505214 174724 104621735923 838 0.8485627499 66202 791251 840 0.8015664476 73920 3295891901 842 0.7876682549 71570 2370917 844 0.8376720882 181460 7295944001 846 0.8142049032 83754 242174417 848 0.8232748309 191648 18770276141 850 0.9701528945 68850 2865899 852 0.8246959945 74976 66856927 854 0.7816720250 118706 831340553 856 0.8510306674 263648 548615176763 858 0.7730683037 55770 33794983 860 0.7875830400 184040 283849393787 862 0.7629563985 160332 3988841561 864 0.8914155653 49248 986113 866 0.7871098852 122972 181431827 868 0.7913892342 123256 1079341177 870 0.8374583079 82650 1305824189 872 0.7561328839 190968 31683162491 874 0.7722875504 180044 34472439539 876 0.8255392548 135780 23908792657 878 0.8059992615 178234 5732050237 880 0.8181553201 134640 7058010781 882 0.8094486988 98784 3607715213 884 0.7567896075 177684 54800797889 886 0.8355161599 239220 113074220731 888 0.8258816962 101232 911045519 890 0.8369225223 100570 105642601 892 0.7741629232 202484 34734355067 894 0.8349591749 82248 83596313 896 0.8173757133 190848 51175902559 898 0.7948385029 204744 25932816499 900 0.8072861180 135000 290994718649 902 0.8232989477 217382 143887883981 904 0.7813795699 218768 71929518179 906 0.8341247493 126840 5993514403 908 0.8038721784 124396 108448177 910 0.8725257404 66430 11447977 912 0.7475902881 153216 384881446787 914 0.7934699183 232156 100197840751 916 0.8514071759 204268 9155647951 918 0.8050224606 136782 35374365181 920 0.8424586115 61640 1763849 922 0.7601528076 214826 58158071267 924 0.8530073203 69300 97746161 926 0.8116795701 221314 35526795583 928 0.8150834574 208800 24269915627 930 0.9064778846 68820 52930403 932 0.8943236869 212496 6725412643 934 0.9991973371 137298 28542649 936 0.8676912530 71136 21181103 938 0.8053687523 217616 221046403007 940 0.8089099343 177660 40714396309 942 0.8067961396 87606 126384917 944 0.8331691839 189744 4182919339 946 0.9314959033 290422 680302968469 948 0.8534806884 193392 505670821001 950 0.8545569452 122550 465470219 952 0.8405042747 119952 235628287 954 0.8998573515 60102 2200661 956 0.7626024207 247604 220062550277 958 0.8529434109 214592 9196163681 960 0.8904686989 120960 10093588667 962 0.8144970096 88504 7634353 964 0.8004216214 107004 17584639 966 0.8283176903 122682 19348856179 968 0.9204665049 279752 259460206361 970 0.8013154534 204670 158734118899 972 0.8225551898 150660 21178988759 974 0.8534921688 303888 568872068111 976 0.9105943329 278160 90346489859 978 0.7903996503 165282 107942471909 980 0.7846347168 117600 1487302123 982 0.8063698833 262194 153969081667 984 0.7799444190 169248 203888107831 986 0.7924196264 225794 89694739373 988 0.8062837244 204516 33384442471 990 0.7913342257 97020 6544493717 992 0.8327256129 248000 65733837647 994 0.8168423482 217686 87037919861 996 0.8046526420 66732 7982237 998 0.8287134801 212574 7185918043 1000 0.8366128339 192000 25270575311 current record for CSG_max with 1000 < q <= 2690: 0.9937793256 @ q=1236 (Gaps in AP - GAP, so to speak )
Last fiddled with by mart_r on 2020-04-30 at 15:10 |
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2020-05-01, 08:51
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#15 |
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Dec 2008
you know...around...
2×11×29 Posts |
Here's something that may or may not be interesting:
Code:
Analysis max. CSG values for each q<=1000, after p is searched to a given point: p <= minimum maximum average (Ø) median 2^10 0.2804444784 0.6807107024 0.4161595621 0.4064414965 2^11 0.3153140952 0.8163798773 0.4479011102 0.4381184715 2^12 0.3431763163 0.8163798773 0.4810577367 0.4669620236 2^13 0.3639186774 0.8469687305 0.5106163332 0.4937025305 2^14 0.4015493440 0.8469687305 0.5417778504 0.5299481585 2^15 0.4292063878 0.8469687305 0.5679300130 0.5598621739 2^16 0.4455266020 0.9438876646 0.6019060399 0.5953644060 2^17 0.4955019575 0.9438876646 0.6276172592 0.6182244977 2^18 0.5136449268 0.9438876646 0.6494452049 0.6377217355 2^19 0.5344779917 0.9438876646 0.6652764872 0.6565675064 2^20 0.5613913893 0.9438876646 0.6814686201 0.6716402626 2^21 0.5715141585 0.9438876646 0.6937490856 0.6821047684 2^22 0.5774364852 0.9701528945 0.7080072985 0.6979367005 2^23 0.5862470282 0.9701528945 0.7194394574 0.7085265144 2^24 0.6158419682 0.9701528945 0.7301409005 0.7173491757 2^25 0.6173926504 0.9991973371 0.7415097777 0.7277374372 2^26 0.6188545442 0.9991973371 0.7497651120 0.7389833874 2^27 0.6592723517 0.9991973371 0.7577502171 0.7486021715 2^28 0.6600619545 0.9991973371 0.7651549239 0.7561863044 2^29 0.6759517875 0.9991973371 0.7723897323 0.7643196755 2^30 0.6759517875 0.9991973371 0.7783479756 0.7697527744 2^31 0.6761477729 0.9991973371 0.7835304099 0.7755264553 2^32 0.6834157728 0.9991973371 0.7891625626 0.7816272396 2^33 0.6938642847 0.9991973371 0.7947508404 0.7869154610 2^34 0.6987121002 0.9991973371 0.7987109313 0.7889756907 2^35 0.7122729187 0.9991973371 0.8041287036 0.7946700265 2^36 0.7122729187 0.9991973371 0.8087488394 0.8009100665 2^37 0.7212478685 0.9991973371 0.8125613682 0.8043811238 2^38 0.7289731501 0.9991973371 0.8180076512 0.8069279875 2^39 0.7289731501 0.9991973371 0.8215276632 0.8121152514 8e11 0.7329439961 0.9991973371 0.8239166643 0.8152880248 For me, it's natural to compare q=30*m for m<=33 here: 22 values are below, 11 above median total; the average of q=30*m for m<=33 at 2^39 is below the average total at 2^38, so at first glance not quite convincing: There seems to be a bias toward that q=2*prime have a higher probability to have CSG_max above median and q=6*m or q=30*m for integer m have a higher probability to have CSG_max below median - BUT only for small q, say q<200 or thereabouts. For higher q, the bias seems no longer present. I shall make the same analysis in smaller clusters of q and check how average and median behaves, later. Here's how the story might continue: Code:
p <= log p z-Ø for z=0.9721 2^10 6.9314718056 0.5559404379 2^11 7.6246189862 0.5241988898 2^12 8.3177661667 0.4910422633 2^13 9.0109133473 0.4614836668 2^14 9.7040605278 0.4303221496 2^15 10.397207708 0.4041699870 2^16 11.090354889 0.3701939601 2^17 11.783502070 0.3444827408 2^18 12.476649250 0.3226547951 2^19 13.169796431 0.3068235128 2^20 13.862943611 0.2906313799 2^21 14.556090792 0.2783509144 2^22 15.249237972 0.2640927015 2^23 15.942385153 0.2526605426 2^24 16.635532333 0.2419590995 2^25 17.328679514 0.2305902223 2^26 18.021826695 0.2223348880 2^27 18.714973875 0.2143497829 2^28 19.408121056 0.2069450761 2^29 20.101268236 0.1997102677 2^30 20.794415417 0.1937520244 2^31 21.487562597 0.1885695901 2^32 22.180709778 0.1829374374 2^33 22.873856958 0.1773491596 2^34 23.567004139 0.1733890687 2^35 24.260151320 0.1679712964 2^36 24.953298500 0.1633511606 2^37 25.646445681 0.1595386318 2^38 26.339592861 0.1540923488 2^39 27.032740042 0.1505723368 This may or may not suggest that the average CSG_max values converge to a value less than 1, and furthermore that the number of gaps > For other values of z, the line fits less good. Anyway, for the thrill of it, some values of z and how the coefficients A and B in the regression log p ~ A*(z-Ø)^B behaves: Code:
z A B 0.95 4.1486 -0.9168 0.96 4.1003 -0.9546 0.97 4.0597 -0.9921 0.98 4.0260 -1.0292 0.99 3.9986 -1.0661 1.00 3.9770 -1.1026 Suggestion to myself: try if the values, especially for the smaller p, fit a little better when using Sum[Ri'(x)] for CSG. I'm full of ideas right now, just not sure if I'm heading in the right direction. Last fiddled with by mart_r on 2020-05-01 at 09:12 Reason: derivative of derivative is abundant:) |
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2020-05-09, 11:46
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#16 |
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Dec 2008
you know...around...
2×11×29 Posts |
Results p<10^12
Data as of 2020-05-04, all p<1012 for q<=1000 have been searched:
Code:
q: common difference in arithmetic progression p+k*q CSG: Cramér-Shanks-Granville ratio via gap/phi(q)/log(p+gap)² CSG_max: maximum value found for CSG up to p=10^12 p: prime preceding the gap current record for CSG_max: 1.0010143609 @ q=152 q CSG_max gap p 2 0.7953486740 456 25056082087 4 0.8056652398 1044 113391385573 6 0.7541322181 462 39895309 8 0.7875867918 2080 144309631099 10 0.8930327253 2450 236455710509 12 0.8455173596 2352 283661812859 14 0.8345982115 2884 26448217657 16 0.9046153418 3728 7194688583 18 0.7887450235 702 194027 20 0.7944296249 1600 7775737 22 0.8617839921 2002 4160719 24 0.8117145259 4392 197036728351 26 0.8652413900 7540 505084610521 28 0.9062903537 8232 888138723221 30 0.8058232068 1980 40846943 32 0.8965150715 3808 11911369 34 0.8182937153 3876 29673503 36 0.7872577337 5400 24166901071 38 0.8518980455 2280 195271 40 0.8613707321 10440 897576340499 42 0.8251402679 3780 305816297 44 0.8085714112 11132 248049290057 46 0.8034522392 7268 640376543 48 0.7973452005 7344 26302298977 50 0.8793539278 4950 19315399 52 0.7811165997 13832 626287370141 54 0.7956494153 7344 6831679457 56 0.8531838024 13272 113946560627 58 0.8160213701 17052 731647597039 60 0.7594431944 8760 457941678127 62 0.7505368847 16740 694602632629 64 0.8613806693 7104 9370547 66 0.7637963086 9834 104493100477 68 0.7981407159 13056 6594265703 70 0.8282785007 11900 42252957959 72 0.8602785358 4824 4344187 74 0.9131005021 9620 26876579 76 0.8416067457 16796 16804480523 78 0.7510340136 9828 13836158729 80 0.8244076217 19680 727457191561 82 0.8163798773 2214 1553 84 0.8017445129 11172 29153099231 86 0.8236614027 9718 19002559 88 0.8173745127 22528 251192223571 90 0.7978827104 14580 962979692377 92 0.8569074437 19320 6775293947 94 0.7540215308 21244 55988532973 96 0.7963941131 17280 203618303897 98 0.8195247347 12936 262621343 100 0.7442402852 20600 265671964073 102 0.7887967496 16626 139972076507 104 0.9499776231 31200 229169128997 106 0.9015411061 33072 342820240309 108 0.8456207760 20196 153489937273 110 0.7957899312 21780 229165433009 112 0.8754122474 19376 2117717087 114 0.8493019884 22116 478998886567 116 0.7977964383 32248 465563693299 118 0.8167041620 20886 1316371417 120 0.8057216311 14040 13628678729 122 0.7947909820 28182 36113593211 124 0.8316652784 30628 57483096991 126 0.9142860299 18270 17061510127 128 0.8323761564 7296 113623 130 0.7938556043 21450 20138027813 132 0.7846464407 10560 92494289 134 0.8397671201 14740 12075073 136 0.7672983613 26928 14785702759 138 0.7924769327 15042 1047660137 140 0.9112585981 31360 425297500759 142 0.8610872285 43026 401037154541 144 0.7893617069 17856 2678906773 146 0.8196507109 23652 494696261 148 0.7830010017 42328 794519516383 150 0.7557605255 21000 279561600257 152 1.0010143609 54264 825353008489 154 0.9369830338 35728 88779374809 156 0.7985008265 13728 165640219 158 0.7606501324 43134 512782039607 160 0.8211887580 36960 328840371359 162 0.8258805846 26244 34294519837 164 0.7924402630 47232 714913847737 166 0.8175587888 42828 94831438649 168 0.7739486136 24864 171996125029 170 0.7905258192 29240 27579604799 172 0.8745407940 38356 8387732083 174 0.8966388328 14616 25666717 176 0.8893387228 32912 2191630061 178 0.7718247316 44856 144798233893 180 0.7968104593 22680 37641351263 182 0.8820202987 27482 1082590961 184 0.8892744577 56856 508307558683 186 0.8021152848 15624 66824477 188 0.7964246226 40044 14217429113 190 0.8735201597 38950 64231886011 192 0.8583746127 11904 2459623 194 0.8234255916 44232 18757576997 196 0.8703957715 44100 46355125469 198 0.7511941018 20196 1560142237 200 0.8255106246 39800 45870059471 202 0.8455991259 26462 48134069 204 0.8383878988 31212 29818321129 206 0.8849004882 20806 3903223 208 0.8637254761 47008 21908990083 210 0.7941670680 27510 464338653979 212 0.8726800198 57028 76983450889 214 0.8300985533 54570 65376711233 216 0.8565309700 38016 60639375773 218 0.8025184444 64746 741341656273 220 0.8516677011 11220 363019 222 0.7476242389 35964 168120545239 224 0.7530876774 27552 300702751 226 0.8205657931 65314 378168298933 228 0.7687388396 35568 102156515693 230 0.8278708905 49910 232943726651 232 0.7860150605 25288 22918543 234 0.7932876948 27144 2934877793 236 0.9437796854 79296 487692833143 238 0.7961571214 47838 73308073691 240 0.8040958748 37680 564376543243 242 0.8312839360 32912 173468021 244 0.8153157728 64172 132595555181 246 0.8801251829 47478 189457586089 248 0.8449133277 22816 3249793 250 0.9603210373 53000 15946776179 252 0.8886298435 37800 35983220659 254 0.7778963787 45974 2545430123 256 0.7699134788 74496 872095415663 258 0.7684771240 45150 305996132599 260 0.7724350668 30160 573522601 262 0.8145777421 79386 778033843151 264 0.8241313527 46200 313621476739 266 0.8801702481 39368 688831433 268 0.7914716927 71020 210484888321 270 0.9385992389 27000 479487689 272 0.7985388488 59568 30497191399 274 0.9241529945 68500 13766905759 276 0.8452548271 33672 1738757609 278 0.8930499724 25854 1925299 280 0.7989596541 52360 222398285827 282 0.8508107698 23406 32332831 284 0.8785941526 66456 12436366727 286 0.7858974077 62920 165094766113 288 0.7935760257 50688 159328991309 290 0.7943100395 67570 931070381161 292 0.8835286349 35624 18463427 294 0.8874698444 31458 834434033 296 0.7407823594 59792 19144263221 298 0.8142218681 71520 38040537103 300 0.8694555188 31500 1746213839 302 0.7889783882 46206 381321631 304 0.9026153946 44688 112884059 306 0.8374812598 13464 403553 308 0.8043192128 57288 38073581723 310 0.8496494922 69750 228639573389 312 0.8318902760 51168 98393397133 314 0.8034115353 51810 676001831 316 0.7761217516 36024 30954479 318 0.8218376546 39114 1952210459 320 0.8298538635 68480 106433008811 322 0.8573533053 54740 3560039459 324 0.7994627901 61560 394806744763 326 0.8083900200 80848 61763668063 328 0.7963256514 70848 17418374759 330 0.7638121358 28380 2288156501 332 0.7948104095 73704 21234656767 334 0.7993791033 100200 859105770221 336 0.7538847566 48720 185386505651 338 0.8637454324 43602 64873867 340 0.8240596233 65280 63699574657 342 0.8010075672 59850 264946609777 344 0.9190160329 66736 1069426291 346 0.7997930054 84078 54543153053 348 0.8268505391 67512 532187265079 350 0.8106891221 61950 91077187501 352 0.7785409404 82720 155422575103 354 0.8053164792 59826 97833706423 356 0.8760991508 102172 151136306521 358 0.7782235660 36516 11215003 360 0.9190759335 23760 13367671 362 0.7879479541 108238 994159631581 364 0.7756310715 51324 2040279533 366 0.8000166747 25986 13943863 368 0.8051615730 105984 753348546229 370 0.7987557798 81400 357568042813 372 0.7936543460 69192 508077732887 374 0.8532053339 58344 951272459 376 0.8393024208 62040 506537617 378 0.7935133452 61236 406541144927 380 0.8062842535 70680 51924372169 382 0.7889373294 90916 49616984707 384 0.7939465677 43392 941956339 386 0.7891241447 86850 24998032091 388 0.8235266859 72556 2009863117 390 0.7826368919 45240 45380958619 392 0.8571708876 75656 9004407101 394 0.8099475511 32308 1536583 396 0.8578841605 68904 172082709217 398 0.8791459095 89152 6737268127 400 0.7989545605 12800 9371 402 0.7868411869 66732 101933130811 404 0.7941196209 83628 9237777071 406 0.8585658511 87696 51121166533 408 0.8204181763 66912 91749328751 410 0.7897091793 46740 225303313 412 0.8036159885 90228 15439142689 414 0.8961928199 80730 221437110397 416 0.8020117468 75296 4013157443 418 0.7948806774 102410 415898213609 420 0.7627980893 26880 209227433 422 0.8690265566 57814 53634703 424 0.7734492416 121688 879624723533 426 0.8161742410 86052 828253660439 428 0.8044283310 40660 5039641 430 0.8013985116 55470 653446711 432 0.8219377815 53568 1734713993 434 0.7722870211 104160 772698979163 436 0.8047788797 102896 36828863651 438 0.7961083251 57816 5663148871 440 0.8792757227 58520 720313157 442 0.7596162182 99450 219117304141 444 0.9438876646 15984 35257 446 0.7775995907 49060 20910913 448 0.7848311396 90944 46689332597 450 0.7619657101 57600 79481983369 452 0.7838385407 97632 17418654119 454 0.7682744177 118948 232873806283 456 0.8859311160 95304 741680341187 458 0.8209257626 71448 305532509 460 0.7705031462 72680 11329574903 462 0.8277181464 44814 1678178797 464 0.8354396498 55680 30933989 466 0.8675896733 26562 70937 468 0.8983741777 95940 671415930377 470 0.8680891345 94000 34320032563 472 0.8363640483 66080 103334411 474 0.8380885352 81528 69987740731 476 0.9122603335 97580 17812528859 478 0.8459786783 58316 24551903 480 0.8369451486 55200 7215375371 482 0.8084758201 85796 1355943101 484 0.7928372491 60984 131951387 486 0.9670602256 66582 897783067 488 0.8236013888 148840 826719013189 490 0.8378578846 82320 31813190909 492 0.7854804768 93480 699003369871 494 0.8392228848 79040 1171149593 496 0.7869001503 98704 8483101717 498 0.7903333451 86652 169488659107 500 0.7914911855 105000 153153439729 502 0.9346253968 41164 540139 504 0.8170280734 50400 974403323 506 0.8272732557 71852 425671457 508 0.8267616819 112776 12711671711 510 0.8611973391 44880 579426871 512 0.7850984980 121344 46897900787 514 0.9225813074 174246 625510735951 516 0.8019834578 72756 12362133493 518 0.8366088676 101010 18527678629 520 0.8696185442 109200 127816392311 522 0.7983405988 46458 120978283 524 0.8097368830 154580 586125879281 526 0.8460548204 168846 968617929451 528 0.8934942692 34848 5998913 530 0.8049360188 57240 107123117 532 0.7920246624 30324 575077 534 0.8161638595 88110 57019930549 536 0.7799025504 138288 179982795691 538 0.9016955220 112980 2457304483 540 0.8029054239 48060 715228027 542 0.8534940538 61246 11964913 544 0.8392434214 126208 33574445479 546 0.8836029793 94458 680726038129 548 0.8034500145 96996 1410813787 550 0.7885921427 109450 275839875067 552 0.7956321590 104880 768279045497 554 0.7914668223 147364 190546085857 556 0.8516820096 150676 98958026977 558 0.9544916211 106020 61428637987 560 0.7749958441 75040 5660034091 562 0.7812147343 151740 274490495683 564 0.8053315904 108852 589938736859 566 0.7891020079 127916 25853082041 568 0.8409819101 71568 37194763 570 0.8015346996 27930 5671207 572 0.7872642046 100100 9913066937 574 0.8355665622 104468 8173667093 576 0.7897361686 103680 227188645297 578 0.7884091107 106352 4694158901 580 0.8716154868 135720 282082451569 582 0.7329439961 103596 607263973321 584 0.7923222032 106872 2504438459 586 0.8159773780 133608 19239163373 588 0.7761971881 58212 1499370799 590 0.8344010904 123900 97104120731 592 0.9093598272 152736 30757758641 594 0.8203596194 103950 333275730829 596 0.8752581666 116220 1578834337 598 0.7972637502 159068 869224163201 600 0.7956697951 19200 196303 602 0.8671990408 55986 8882693 604 0.8070806533 103284 932676103 606 0.7796492138 96960 67559839063 608 0.8125159769 141664 48492135667 610 0.8365143363 40260 1372451 612 0.7978540809 44064 23167169 614 0.8275383515 68768 14281613 616 0.7562342777 116424 99877977587 618 0.8265107359 111240 142939098451 620 0.7625254531 44640 6020933 622 0.8063729000 93300 245534483 624 0.9394014419 132288 577632351979 626 0.8240605983 195312 933121023811 628 0.8690691013 152604 20089808047 630 0.7878195018 83790 635068094299 632 0.8457792089 182648 266552475209 634 0.8321349317 178154 201487337099 636 0.8465112163 94128 11000930573 638 0.7538727012 93148 1327646743 640 0.9120077454 55040 4602251 642 0.8152602768 77040 1475945477 644 0.8303242949 97244 1403478863 646 0.9148101139 191862 524463691699 648 0.8487263784 57024 45602917 650 0.7783532479 57850 43857397 652 0.8380466032 132356 3876681503 654 0.9214740453 51666 9881863 656 0.8450147043 194832 454517973809 658 0.8049383681 151998 228935733461 660 0.8043599214 95700 696335516473 662 0.7812198551 195952 940473435469 664 0.8497732615 179944 108343097587 666 0.9612073070 137196 145879569457 668 0.8291122833 161656 33463509787 670 0.8588802430 146730 111632773561 672 0.8377544361 92064 24553355279 674 0.8927385746 154346 7102999643 676 0.7911246648 81120 74589533 678 0.8188167676 101700 16846380763 680 0.7847062189 129880 110374441477 682 0.8756801286 157542 43180032209 684 0.8371047755 63612 139850671 686 0.8425141547 118678 3207660733 688 0.7914089252 87376 74464177 690 0.8298009290 93150 92923597009 692 0.8099695701 189608 213400291319 694 0.9352046150 222080 238517976413 696 0.8663493208 64728 85359893 698 0.7930566851 198930 456923141659 700 0.8284455357 136500 239460526523 702 0.9106053914 148122 827875560931 704 0.8202954082 187264 397943965597 706 0.8695438095 40242 55201 708 0.8977861205 144432 273087013487 710 0.7724598204 149810 269015016161 712 0.8199108541 213600 652989609751 714 0.7953230813 113526 694348824997 716 0.7831859227 193320 272750735171 718 0.7661030339 186680 214029806201 720 0.8760847971 119520 377221918061 722 0.7724554548 201438 982598073973 724 0.7975329263 110772 339112381 726 0.8799338964 137940 391674855421 728 0.9518517909 184184 180789356273 730 0.8169767948 59130 7609781 732 0.8289374951 34404 479797 734 0.8603414239 198180 78573408271 736 0.7940567828 36064 49669 738 0.8187851952 69372 144447397 740 0.9215487467 202020 959204145013 742 0.8270690786 48972 912367 744 0.7697508611 124992 197934069341 746 0.8040409658 181278 49168511023 748 0.7830564314 139128 17115875771 750 0.8359892306 106500 91377216071 752 0.7749013078 128592 1668673339 754 0.7901283265 199810 821226058453 756 0.7984514297 71820 728533909 758 0.8307863368 161454 7035777923 760 0.8587348951 151240 54915038317 762 0.7947601914 132588 149362737379 764 0.8072228398 182596 39444378481 766 0.8360220240 124092 363645049 768 0.8159361794 104448 5146249133 770 0.8561631304 154770 830060466467 772 0.7934001992 214616 336250303541 774 0.7963577306 77400 338022701 776 0.8694867562 95448 21931331 778 0.7896427008 161046 9056973697 780 0.7773942238 109200 558379404841 782 0.7925574832 168912 48563547259 784 0.8187678710 40768 152791 786 0.7375163313 128904 182041921063 788 0.8598576323 115836 112344431 790 0.7632748154 179330 827400226427 792 0.7809066212 131472 318121728761 794 0.8737191630 146096 839726627 796 0.8171350137 216512 171358508429 798 0.8189774650 110124 68522931313 800 0.7854380237 124000 4429597201 802 0.8127895345 231778 394291297993 804 0.7850960183 134268 113158700561 806 0.9079408402 82212 7638601 808 0.7877421483 113120 169209149 810 0.8116850129 89910 6836640043 812 0.8851736046 157528 9883553821 814 0.7938088485 104192 196064567 816 0.8066643398 61200 29890303 818 0.8335856530 112884 81576293 820 0.8731640737 90200 63450923 822 0.8762643516 110970 2349421741 824 0.8675619063 149144 821531663 826 0.7608164263 191632 482975333977 828 0.7652805026 90252 1510362617 830 0.9773893526 154380 3391062847 832 0.8327364626 114816 169459867 834 0.8070598355 81732 208384291 836 0.7538505214 174724 104621735923 838 0.8485627499 66202 791251 840 0.8015664476 73920 3295891901 842 0.7876682549 71570 2370917 844 0.8376720882 181460 7295944001 846 0.8142049032 83754 242174417 848 0.8232748309 191648 18770276141 850 0.9701528945 68850 2865899 852 0.8246959945 74976 66856927 854 0.7816720250 118706 831340553 856 0.8510306674 263648 548615176763 858 0.7730683037 55770 33794983 860 0.8197281512 208980 917866963313 862 0.7629563985 160332 3988841561 864 0.8914155653 49248 986113 866 0.7871098852 122972 181431827 868 0.7913892342 123256 1079341177 870 0.8374583079 82650 1305824189 872 0.7561328839 190968 31683162491 874 0.7722875504 180044 34472439539 876 0.8255392548 135780 23908792657 878 0.8059992615 178234 5732050237 880 0.8181553201 134640 7058010781 882 0.8094486988 98784 3607715213 884 0.7567896075 177684 54800797889 886 0.8355161599 239220 113074220731 888 0.8258816962 101232 911045519 890 0.8369225223 100570 105642601 892 0.7741629232 202484 34734355067 894 0.8349591749 82248 83596313 896 0.8173757133 190848 51175902559 898 0.7948385029 204744 25932816499 900 0.8072861180 135000 290994718649 902 0.8232989477 217382 143887883981 904 0.7813795699 218768 71929518179 906 0.8341247493 126840 5993514403 908 0.8038721784 124396 108448177 910 0.8725257404 66430 11447977 912 0.7593864429 166896 993555184957 914 0.7934699183 232156 100197840751 916 0.8514071759 204268 9155647951 918 0.8050224606 136782 35374365181 920 0.8424586115 61640 1763849 922 0.7601528076 214826 58158071267 924 0.8530073203 69300 97746161 926 0.8116795701 221314 35526795583 928 0.8150834574 208800 24269915627 930 0.9064778846 68820 52930403 932 0.8943236869 212496 6725412643 934 0.9991973371 137298 28542649 936 0.8676912530 71136 21181103 938 0.8053687523 217616 221046403007 940 0.8630893831 239700 852543477769 942 0.8067961396 87606 126384917 944 0.8331691839 189744 4182919339 946 0.9314959033 290422 680302968469 948 0.8534806884 193392 505670821001 950 0.8545569452 122550 465470219 952 0.8405042747 119952 235628287 954 0.8998573515 60102 2200661 956 0.7626024207 247604 220062550277 958 0.8529434109 214592 9196163681 960 0.8904686989 120960 10093588667 962 0.8144970096 88504 7634353 964 0.8004216214 107004 17584639 966 0.8283176903 122682 19348856179 968 0.9204665049 279752 259460206361 970 0.8013154534 204670 158734118899 972 0.8225551898 150660 21178988759 974 0.8534921688 303888 568872068111 976 0.9105943329 278160 90346489859 978 0.7903996503 165282 107942471909 980 0.7846347168 117600 1487302123 982 0.8063698833 262194 153969081667 984 0.7799444190 169248 203888107831 986 0.7924196264 225794 89694739373 988 0.8062837244 204516 33384442471 990 0.7913342257 97020 6544493717 992 0.8327256129 248000 65733837647 994 0.8168423482 217686 87037919861 996 0.8046526420 66732 7982237 998 0.8287134801 212574 7185918043 1000 0.8366128339 192000 25270575311 current record for CSG_max with 1000 < q <= 2690: 0.9961616621 / p=131264869717 @ q=1502 New code in the attachment, if anyone wants to check if I'm doing things right. (Ponder this: why is the search slower when the interval is larger? When I use v& = 250*106, it takes more time per q per 1e9 than with e.g. v& = 100*106.) |
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2020-05-23, 12:57
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#17 |
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Dec 2008
you know...around...
27E16 Posts |
An update before a long weekend
Just letting you know, I'm still on it.
All q<=2690 have now also been searched to p<1012. For q<=1000, only new results for 1012<p<3*1012 are shown in the table. Code:
q: common difference in arithmetic progression p+k*q
CSG: Cramér-Shanks-Granville ratio via gap/phi(q)/log(p+gap)²
CSG_max: maximum value found for CSG up to p=3*10^12 for q<=1000
and up to p=1*10^12 for 1002<=q<=2690
p: prime preceding the gap
current record for CSG_max: 1.0010143609 @ q=152
q CSG_max gap p
2 0.7975364451 652 2614941710599
4 0.8156352348 1296 1742590107893
6 0.8043096326 1302 2267675747429
36 0.7953959798 7776 2488620283151
44 0.8161839043 13024 1850366919097
52 0.8552310627 16588 2219314413889
60 0.7669174562 10020 2572440924871
78 0.7743337878 14430 1263973956209
96 0.8182152357 20448 1369965278489
100 0.7680513916 23700 1154488219009
108 0.8602004012 24840 1995773049461
120 0.8282174817 21720 2708602511759
132 0.7859399899 25080 1847468163427
144 0.8107023756 31248 2026608933563
164 0.8441634292 51988 1121341862779
168 0.8433419790 31080 1080904914041
188 0.8027478817 58468 1658375170513
204 0.8539893393 41820 1030953050879
222 0.7849812426 46398 2775690916351
228 0.7808534284 46056 2692471834747
256 0.7763078423 81408 2695929230861
260 0.8048824266 61100 1631014483229
296 0.8053960245 92056 1720183292131
316 0.7812949989 99856 2696940430573
320 0.8711507167 87360 1432030776599
324 0.8811825528 78408 2922713649013
332 0.8098772215 106572 2004292884031
336 0.7795787395 58800 1490297805131
354 0.8154566619 73278 1223614030909
362 0.8103149561 119098 2570663585143
378 0.7960964800 68796 1927024584677
382 0.7974241509 123768 2586552507463
400 0.8031013151 104800 2528142047017
404 0.8092199728 132512 2672534840891
410 0.8104490914 104550 2146419881959
420 0.8137078518 63840 2602583597491
424 0.7942461165 129744 1481798051813
426 0.8289323077 93720 2196617261591
442 0.7598300383 119782 2781776304577
446 0.8458889929 144058 1068393787429
460 0.7789301939 106260 1233214813793
464 0.8572536024 146624 1001714625503
482 0.8414206048 161470 1907903025913
496 0.8681833256 167648 2084041939613
518 0.8616203249 146076 1469437363843
524 0.8373313497 172920 1736690999713
560 0.8286810737 131040 2907735010097
562 0.8012678143 183774 2689292102213
570 0.8077786761 90630 1325924145547
606 0.7832381303 129078 2928289981961
614 0.8278175055 206304 2477198425619
630 0.8008557008 90090 1375553927617
638 0.7613227599 168432 1613175082811
658 0.8130657611 173712 1211146285927
700 0.8448666880 156100 1121946737221
716 0.8167618692 234848 2200662519749
730 0.8354837675 190530 1662765783331
736 0.8188024802 228896 1733418109697
738 0.8397515047 158670 1533579302309
752 0.8198735059 245152 2396322870481
764 0.8457379887 249828 1284203453959
772 0.8407408933 247812 1077217612519
774 0.8133175100 162540 1699086152611
776 0.9050703906 277032 1825864325267
786 0.7769364381 162702 2115479982437
788 0.8655999552 274224 2219521221103
792 0.7890711683 149688 1621645314451
806 0.9415866545 259532 1040072922719
828 0.8617772785 182988 2073720212383
836 0.7607113183 216524 1628172420059
842 0.8318604579 268598 1100638524959
844 0.8385676885 288648 2710003170233
872 0.8379003012 284272 1481278956049
874 0.8527915219 262200 1262666597447
878 0.8268563093 293252 2281019340629
896 0.8323652240 261632 2662613002121
912 0.7999319242 180576 1441530403283
918 0.8142665500 182682 1322501588087
922 0.8143471563 291352 1293675650599
926 0.8700093869 316692 1550438309309
954 0.9313516973 224190 1156330148921
972 0.8329651188 218700 2306583801539
980 0.8321288844 223440 1893277237571
982 0.8406561335 332898 2219125353463
984 0.7883655576 201720 1908143874971
998 0.8542800442 331336 1318358219977
1002 0.8173324542 101202 243721099
1004 0.9335109890 277104 38179649843
1006 0.7986257468 205224 6697982497
1008 0.8180657107 89712 298174159
1010 0.8102755199 164630 6136972889
1012 0.8469913079 273240 574841273183
1014 0.8057706816 53742 2183809
1016 0.7778067456 252984 107806726613
1018 0.8263188853 293184 300287895043
1020 0.8381299562 79560 230533159
1022 0.7867645035 194180 24021101957
1024 0.9585073790 104448 2062273
1026 0.9039253698 179550 56651445803
1028 0.8731337653 302232 195981436499
1030 0.8443177018 214240 67697842111
1032 0.7919147337 123840 2340188621
1034 0.8470522110 214038 15092955791
1036 0.7825387960 167832 4749806249
1038 0.9575655965 83040 7777997
1040 0.8744748768 237120 347231600003
1042 0.8213473341 189644 1416993209
1044 0.7691513477 184788 410234894429
1046 0.8218743660 209200 3891938893
1048 0.8601385196 210648 2659949681
1050 0.7607034722 127050 286198762259
1052 0.7923620723 250376 46217768657
1054 0.8368529001 154938 338215609
1056 0.7644151486 89760 208497077
1058 0.8307721283 314226 747797555503
1060 0.7824557394 155820 3177411277
1062 0.7977441927 111510 505733909
1064 0.8564546152 156408 849704521
1066 0.7982755475 266500 284078285317
1068 0.8478768334 97188 68618423
1070 0.8264808233 265360 893218919371
1072 0.7754552986 273360 166587461267
1074 0.8686307359 110622 163626431
1076 0.7670245009 111904 14512039
1078 0.8511140984 113190 53349139
1080 0.8799842835 59400 4395199
1082 0.7680217132 96298 4050703
1084 0.8055816331 275336 84347645843
1086 0.8099434951 141180 3600296621
1088 0.9215699569 280704 39153022523
1090 0.7626480453 235440 407085806213
1092 0.8554992672 53508 2459029
1094 0.8095511766 65640 130411
1096 0.8213283778 289344 112671986677
1098 0.7816667884 200934 402811030067
1100 0.8339897725 231000 268074297247
1102 0.7387317926 76038 1532449
1104 0.7794659089 172224 75999313087
1106 0.8205856862 263228 234493195931
1108 0.8310993353 152904 84691319
1110 0.8598529624 89910 188373931
1112 0.7361306416 275776 206055104221
1114 0.7808359165 314148 481344775321
1116 0.8217937622 123876 770418163
1118 0.8601075905 216892 5180204077
1120 0.8854848018 248640 554542566943
1122 0.8264648520 124542 2657104391
1124 0.7998804113 171972 323087201
1126 0.8239936780 248846 11679983813
1128 0.8415828599 172584 17868227233
1130 0.7767269864 265550 993848893859
1132 0.8593262063 261492 12239261357
1134 0.9074951221 136080 2202840361
1136 0.9282887980 197664 293985487
1138 0.7790190677 334572 875195588849
1140 0.8076628284 111720 3294785161
1142 0.8700860381 238678 3367566031
1144 0.8223236332 260832 145906334257
1146 0.8317407053 113454 169035079
1148 0.8428018553 268632 155339123747
1150 0.8666095971 158700 724310183
1152 0.8352721397 175104 14039343203
1154 0.8594648293 153482 44201357
1156 0.7948368197 194208 1599584023
1158 0.8443111047 81060 7282003
1160 0.7892622029 214600 50021176927
1162 0.8204889884 270746 176705807177
1164 0.8102121131 182748 33540401473
1166 0.7784678789 257686 90657446557
1168 0.9572586699 153008 17010893
1170 0.7729929107 87750 419009483
1172 0.8229533295 298860 67591400683
1174 0.8060000295 190188 518421439
1176 0.8276281207 151704 13921176817
1178 0.7860532263 266228 75244938953
1180 0.7739208075 177000 4384360093
1182 0.7603415472 213942 432013072727
1184 0.8257881683 355200 737796275731
1186 0.7787172151 348684 879010204327
1188 0.8341177364 218592 521845216861
1190 0.7673368007 197540 175726677683
1192 0.8066264649 241976 5973880721
1194 0.8307393169 239994 537249220913
1196 0.8485558966 307372 237249620227
1198 0.8666707618 341430 140276755583
1200 0.8052107557 180000 301057281797
1202 0.7892545849 168280 153591049
1204 0.8024916553 198660 4217467523
1206 0.8113571022 170046 9797297701
1208 0.7764456913 269384 27754075967
1210 0.9195212184 151250 249315263
1212 0.8975392861 99384 16719533
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1962 0.8578620403 392400 345609175889
1964 0.8345424979 595092 518696590459
1966 0.8878075384 440384 5764421087
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1972 0.9263154811 605404 536212777627
1974 0.8058616819 173712 381960377
1976 0.8133574376 468312 162651150481
1978 0.7688230914 195822 16041257
1980 0.8040018986 138600 169811309
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1986 0.8786959000 162852 18787777
1988 0.8778215869 447300 49713998333
1990 0.8857322728 222880 54878167
1992 0.8009272405 225096 975153437
1994 0.8396915640 502488 44186280899
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1998 0.7808272591 291708 26780243779
2000 0.8303456888 450000 201178467727
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2004 0.8162851392 390780 458416204973
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2008 0.8486375398 301200 151695521
2010 0.8342503869 190950 1102112779
2012 0.7734880161 150900 981241
2014 0.7671073980 410856 24475888897
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2018 0.8494843501 571094 164359880327
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2154 0.8311032470 174474 27143603
2156 0.7803814971 409640 71872165709
2158 0.8375276941 308594 253146317
2160 0.9376729050 380160 332714549693
2162 0.7908718147 473478 36566435363
2164 0.8154457889 393848 1527717791
2166 0.7984010056 379050 276560036659
2168 0.7659054961 513816 66683488213
2170 0.9431982536 288610 897296623
2172 0.7720492907 373584 181441374769
2174 0.8078314291 221748 7806221
2176 0.8449114551 361216 747554851
2178 0.8055899389 280962 9625032539
2180 0.8018843811 270320 378596093
2182 0.9210391264 473494 2701520953
2184 0.7654168402 100464 3495823
2186 0.8016100263 413154 2723037113
2188 0.8976738587 676092 254424267029
2190 0.8363533681 208050 1059796799
2192 0.8351214808 624720 244199115887
2194 0.8684701090 636260 169209614501
2196 0.7772574036 223992 488025271
2198 0.7891215994 419818 22589954983
2200 0.8883427140 228800 61787291
2202 0.7887802821 118908 1588801
2204 0.8458308451 372476 1194713543
2206 0.7848417164 337518 379223861
2208 0.8199545230 295872 6796402447
2210 0.9119845144 335920 3243341317
2212 0.8586024767 387100 3399889981
2214 0.8471435342 414018 206470904039
2216 0.8021249047 285864 63239083
2218 0.8778924796 678708 296412366823
2220 0.7880128324 137640 36399353
2222 0.7649112784 226644 29674187
2224 0.8295824011 420336 2013164977
2226 0.8709747186 333900 58154921369
2228 0.8376555482 434460 2394970429
2230 0.8243787540 294360 511045949
2232 0.8107895334 214272 208930949
2234 0.8638791103 355206 216493477
2236 0.8503672287 221364 9310507
2238 0.8901411615 467742 348134738267
2240 0.8055637999 356160 26314798501
2242 0.8226424209 363204 852887743
2244 0.8681184286 195228 138150269
2246 0.8474866418 572730 45551492071
2248 0.8250100800 512544 16922727467
2250 0.8254644474 265500 11355705887
2252 0.8218322114 682356 636232475033
2254 0.8542551982 513912 120644298881
2256 0.8629248633 196272 42919049
2258 0.7891834514 426762 3227872051
2260 0.7749354667 187580 13560257
2262 0.8158831853 291798 10448276911
2264 0.8420737848 713160 794388396031
2266 0.8338951629 317240 243635459
2268 0.8481414977 233604 898653529
2270 0.8862233708 497130 65827577419
2272 0.7644786846 483936 21130374217
2274 0.8764404650 450252 209476646777
2276 0.7764284024 546240 64234545953
2278 0.7532676674 435098 14358928049
2280 0.8268772522 326040 230604681031
2282 0.7882391727 561372 569736287669
2284 0.8117097930 678348 573664146221
2286 0.8637388287 137160 1831987
2288 0.7869488679 526240 289856428051
2290 0.7920970940 178620 6568031
2292 0.7649375313 339216 30949412261
2294 0.8325578826 346394 333953699
2296 0.7792436901 523488 308002613761
2298 0.7541889590 358488 68022309503
2300 0.8125797241 522100 543376141813
2302 0.8141515820 347602 233021161
2304 0.8594340588 481536 537492065717
2306 0.9154130802 219070 1598617
2308 0.7894156522 660088 501816932311
2310 0.7799182950 78540 1873513
2312 0.8674247228 462400 4102401619
2314 0.7925051756 520650 67980657709
2316 0.8592528052 252444 311826077
2318 0.8561397222 222528 5240101
2320 0.8718135463 584640 760793625643
2322 0.8588823907 390096 44148299231
2324 0.7732456619 525224 257267005013
2326 0.8557835135 397746 484497023
2328 0.8945424266 311952 1795974079
2330 0.8328593105 370470 3222623119
2332 0.7693951284 345136 1045858357
2334 0.8484177520 163380 6778033
2336 0.8112627080 546624 31856145323
2338 0.8585159682 586838 238401125849
2340 0.7546329465 262080 46136691787
2342 0.9229298450 733046 206761566857
2344 0.8076481205 696168 628074675289
2346 0.7925852775 326094 31546997333
2348 0.8358341918 612828 72860992511
2350 0.8283901892 192700 7857313
2352 0.8449394678 359856 85762575343
2354 0.8123041008 211860 6279617
2356 0.9064519315 438216 1543003597
2358 0.7788593874 124974 1569307
2360 0.7757682740 500320 281201402173
2362 0.7291885369 621206 466877434043
2364 0.7783902085 144204 4598203
2366 0.8215129092 288652 259406821
2368 0.8829131011 748288 602114594209
2370 0.8865971719 177750 60713161
2372 0.8035193297 389008 604842781
2374 0.7667369906 678964 736261556533
2376 0.8810062237 299376 2721742963
2378 0.7927634714 670596 861622073677
2380 0.7745299000 299880 5638758737
2382 0.7680549495 200088 75057643
2384 0.8282466611 717584 559793447813
2386 0.8772966704 262460 7327763
2388 0.8058200406 355812 17966184359
2390 0.8975224664 255730 32354719
2392 0.8043241802 581256 229668981863
2394 0.8090253541 105336 1327111
2396 0.8580344286 618168 45611223223
2398 0.7865336675 316536 241507381
2400 0.7635251277 352800 467043338761
2402 0.9031048934 384320 150433103
2404 0.8137395535 497628 6367483051
2406 0.8520553527 120300 467867
2408 0.7678051922 553840 414680346433
2410 0.7780260570 400060 11248596199
2412 0.8405729453 313560 2662138627
2414 0.7711131520 557634 108509711657
2416 0.8299590654 645072 112907977309
2418 0.7618561842 372372 206729972041
2420 0.7905715096 326700 2577433259
2422 0.8737056997 636986 349313358767
2424 0.8463147292 509040 809631798277
2426 0.8648306484 788450 815028696011
2428 0.7900032871 463748 3612270863
2430 0.7915394356 247860 3522895501
2432 0.8680034376 437760 1221059317
2434 0.8000074355 705860 499446658943
2436 0.8087405849 158340 25720103
2438 0.8163448566 402270 1031162347
2440 0.8904128070 470920 15615750541
2442 0.8619274920 344322 16972376501
2444 0.7868834861 630552 501782372369
2446 0.7673643592 511214 13811727857
2448 0.7916674170 119952 1139227
2450 0.7976379815 502250 777219739931
2452 0.9585963388 210872 453137
2454 0.8572029328 171780 6223667
2456 0.8258166895 456816 1707851083
2458 0.8194532445 297418 28965733
2460 0.8244748324 383760 515369429777
2462 0.8511266276 679512 116020335329
2464 0.7706291229 544544 606227974559
2466 0.7963644070 424152 124573828051
2468 0.9329576496 244332 1903301
2470 0.7435891544 479180 725601206171
2472 0.8119016402 499344 837629197919
2474 0.8361829894 482430 2414960227
2476 0.7960159596 661092 180959311921
2478 0.8569843105 344442 27315473041
2480 0.8194362764 540640 242838561517
2482 0.8501855564 402084 629876623
2484 0.7552473256 375084 75041495759
2486 0.8124169631 504658 16898103349
2488 0.7859003369 686688 337606158101
2490 0.8037901955 313740 39233353787
2492 0.8083494058 221788 9787039
2494 0.7827044010 177074 878873
2496 0.8199349432 476736 890407957763
2498 0.8300985187 262290 7873469
2500 0.8459473672 372500 1297710119
2502 0.8787444409 330264 1789037759
2504 0.8734452768 280448 8967173
2506 0.8044716080 473634 15732838523
2508 0.8000543786 378708 136621802293
2510 0.8296760210 542160 126417684163
2512 0.8467662766 195936 623671
2514 0.8365770068 372072 10401056257
2516 0.8076722078 626484 185892132809
2518 0.8782289295 458276 699575441
2520 0.7815450228 115920 9196807
2522 0.8104566307 514488 15661557383
2524 0.8313015963 373552 158677777
2526 0.7801749658 255126 370356221
2528 0.7756992109 723008 739035352871
2530 0.7972433038 349140 4878244649
2532 0.7679961125 177240 15619469
2534 0.7845873694 572684 195163249889
2536 0.7832586885 705008 388369699811
2538 0.8136339962 246186 200232311
2540 0.8004875429 594360 612283207313
2542 0.8989147199 394010 199219799
2544 0.8400237991 172992 6629387
2546 0.8399063742 621224 68610331883
2548 0.7523453472 443352 31676007821
2550 0.8196549026 280500 11029796251
2552 0.7751988286 658416 911302288367
2554 0.7778223327 574650 28189790411
2556 0.7905006100 173808 10451179
2558 0.8567957666 828792 887593062737
2560 0.8212147618 529920 79821713953
2562 0.7586665234 335622 58222542601
2564 0.7928609611 597412 34435934821
2566 0.8424737721 713348 144959825909
2568 0.8061790647 210576 41679137
2570 0.9619459674 354660 173713313
2572 0.8130912819 733020 321913725169
2574 0.7915056411 375804 142064839619
2576 0.7905255410 602784 467861927717
2578 0.7887216191 742464 550708199563
2580 0.7743905635 291540 19029001837
2582 0.9437094381 818494 182400714409
2584 0.8274264593 552976 28863485671
2586 0.8373883588 426690 37263350507
2588 0.8145755184 768636 545439097163
2590 0.7694910475 427350 102509369951
2592 0.8487067279 427680 30786910439
2594 0.9041436410 365754 46717493
2596 0.8053648183 576312 61189450727
2598 0.8076647220 470238 187849378111
2600 0.8273546596 221000 17331641
2602 0.8401129167 572440 8765438179
2604 0.8326267909 221340 221053711
2606 0.8221688680 719256 180904315547
2608 0.7968833417 469440 1815973217
2610 0.7977052404 373230 288089409547
2612 0.7707861529 417920 716956337
2614 0.8594118059 784200 301693020571
2616 0.7315603326 164808 10134331
2618 0.8412065298 314160 367727071
2620 0.7613793196 589500 707529794791
2622 0.7390603437 401166 234187524581
2624 0.7732717061 663872 176800661201
2626 0.7653767382 603980 137080434437
2628 0.7765421620 420480 74507762587
2630 0.8408173934 649610 619119337283
2632 0.7923082847 626416 418876194211
2634 0.8451563971 521532 336262377679
2636 0.8607846111 229332 1281899
2638 0.8167139746 582998 12795204341
2640 0.8226472501 290400 15836332901
2642 0.7854687566 435930 803368823
2644 0.7685865001 727100 423129900653
2646 0.8781688819 412776 67465005107
2648 0.8641502338 701720 59115954797
2650 0.8209442976 445200 8263436131
2652 0.8158978442 434928 276568689209
2654 0.7989051547 398100 262029809
2656 0.7993877234 172640 200591
2658 0.8279609779 465150 88792250263
2660 0.8158176891 452200 100019816647
2662 0.8225958214 324764 69628499
2664 0.8279695897 535464 761878688143
2666 0.7746957069 610514 72657935507
2668 0.8726439435 664332 62481289817
2670 0.8646908085 416520 229185148609
2672 0.7877402928 790912 873917725651
2674 0.7922077633 574910 90681187253
2676 0.8134087029 503088 289469802851
2678 0.8078425394 297258 33589921
2680 0.8165051269 450240 8397761893
2682 0.7903008119 219924 48541973
2684 0.7815422369 523380 18175376237
2686 0.8114513610 539886 10655490721
2688 0.8109550571 325248 8405709199
2690 0.8155768850 169470 943429
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2020-06-03, 18:11
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#18 |
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Dec 2008
you know...around...
10011111102 Posts |
Just for fun, I let my program look for q up to 3*105 for a couple millions of p, and within one day, I found more than 50 new extraordinarily large gaps (larger than
I'll try to set a new record here in terms of CSG and probably post some results by Friday. BTW, q<=1000 currently @ p=4.8*1012, q<=2690 @ p=1.8*1012, no major findings in the last few days. Progressing. |
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2020-06-07, 12:30
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#19 |
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Dec 2008
you know...around...
2×11×29 Posts |
prob·a·bly adv. very likely; without much doubt (Webster's New World basic dictionary of American English)
If a number P between 0 and 1 should be assigned in this regard, how large would it be? Anyway, here's some data for posterity: Code:
gap/phi(q)/ CSG-method
gap p p' k q r log²(p') Sum Ri'(x) who/year
26026560 150211753 176238313 112 232380 94273 1.1658890306 1.1753290815 Raab 2020
3906628 190071823 193978451 209 18692 11567 1.1480589845 1.1491888083 Kourbatov/Wolf 2017
12749520 202722071 215471591 210 60712 4703 1.1408583553 1.1443595696 Raab 2020
44221268 19019009 63240277 182 242974 67037 1.1281678511 1.1916358202 Raab 2020
21106128 1560734261 1581840389 167 126384 18245 1.1170554360 1.1177296369 Raab 2020
8083028 344107541 352190569 206 39238 29519 1.1134625422 1.1147048561 Kourbatov/Wolf 2017
31135962 916198957 947334919 143 217734 192019 1.1049327614 1.1066623864 Raab 2020
43706268 403761601 447467869 146 299358 227017 1.1039772763 1.1095079567 Raab 2020
58244058 219789979 278034037 139 419022 222451 1.1031048845 1.1158890335 Raab 2020
9403290 1015173661 1024576951 117 80370 20191 1.0992710599 1.0997196593 Raab 2020
20655000 7827217 28482217 81 255000 177217 1.0953885874 1.1632317742 Raab 2020
63203910 85252241 148456151 165 383054 214253 1.0875048872 1.1170637202 Raab 2020
12312360 42545843 54858203 115 107064 41435 1.0871339798 1.1018732870 Raab 2020
76697040 325087801 401784841 210 365224 38441 1.0870612491 1.0982670091 Raab 2020
35920626 284354281 320274907 119 301854 7813 1.0860305010 1.0924116630 Raab 2020
13720800 3216881 16937681 120 114340 15361 1.0829962394 1.1674502497 Raab 2020
15670164 57747743 73417907 177 88532 24879 1.0792088227 1.0928849191 Raab 2020
208650 3415781 3624431 65 3210 341 1.0786589153 1.0821910132 Kourbatov/Wolf 2017
40233294 129394039 169627333 129 311886 273235 1.0778496711 1.0925310542 Raab 2020
42576716 53707037 96283753 182 233938 135235 1.0771626660 1.1085952932 Raab 2020
26994402 68872591 95866993 171 157862 44759 1.0760433707 1.0943950612 Raab 2020
18491724 508984297 527476021 138 133998 59893 1.0741607074 1.0759988158 Raab 2020
2157480 13074917 15232397 78 27660 19397 1.0716522452 1.0809485789 Kourbatov/Wolf 2019
24502010 675559229 700061239 205 119522 20885 1.0710260557 1.0728404154 Raab 2020
3415794 376981823 380397617 201 16994 3921 1.0703375544 1.0707668266 Kourbatov/Wolf 2017
72750990 279155309 351906299 195 373082 89973 1.0701202187 1.0822289562 Raab 2020
10876660 18970891 29847551 155 70172 24451 1.0698062013 1.0960456465 Raab 2020
48318616 457558447 505877063 212 227918 127021 1.0692343217 1.0744489116 Raab 2020
1530912 728869417 730400329 222 6896 3593 1.0684247390 1.0684935933 Kourbatov/Wolf 2017
11563370 381674801 393238171 131 88270 83591 1.0679043611 1.0694410998 Raab 2020
67002754 155635027 222637781 169 396466 220355 1.0673928908 1.0862011035 Raab 2020
34710336 646336727 681047063 216 160696 17415 1.0671818425 1.0698537690 Raab 2020
60029536 236847133 296876669 203 295712 277533 1.0668680315 1.0787516718 Raab 2020
31111720 338212681 369324401 166 187420 107001 1.0665081217 1.0711276926 Raab 2020
45480858 37855579 83336437 177 256954 83341 1.0642247130 1.1053573836 Raab 2020
52973904 272681197 325655101 136 389514 21397 1.0619276093 1.0712027205 Raab 2020
21486816 58954163 80440979 117 183648 3155 1.0598554173 1.0769849413 Raab 2020
1896608 164663 2061271 112 16934 12257 1.0598397341 1.1852239238 Kourbatov/Wolf 2017
55129728 131328623 186458351 192 287134 108385 1.0588409893 1.0773034386 Raab 2020
30580280 31606847 62187127 170 179884 127147 1.0557711073 1.0918855069 Raab 2020
10355604 856609109 866964713 183 56588 36553 1.0545686348 1.0551433620 Raab 2020
5403024 262789987 268193011 132 40932 6547 1.0541831039 1.0552109864 Raab 2020
20332800 88927171 109259971 96 211800 182971 1.0537979234 1.0649986104 Raab 2020
132625590 2839657 135465247 115 1153266 533125 1.0536024200 1.1675846988 Raab 2020
41112864 1720833797 1761946661 234 175696 67173 1.0533569871 1.0544909778 Raab 2020
10723372 1626559621 1637282993 202 53086 4581 1.0503858509 1.0506827685 Raab 2020
14065200 965324803 979390003 180 78140 61383 1.0502207536 1.0509147496 Raab 2020
31303064 734306093 765609157 194 161356 136293 1.0501770849 1.0522589060 Raab 2020
28427040 565631527 594058567 171 166240 83047 1.0484424049 1.0509123457 Raab 2020
7230930 130172279 137403209 147 49190 15539 1.0468373915 1.0497240560 Kourbatov/Wolf 2019
61008404 543640997 604649401 214 285086 267081 1.0468336353 1.0521974766 Raab 2020
17611524 87652883 105264407 153 115108 55695 1.0465179793 1.0564849581 Raab 2020
9436848 8241139 17677987 141 66928 8995 1.0463975066 1.0892125979 Raab 2020
4575906 20250677 24826583 101 45306 44201 1.0463153374 1.0581819483 Kourbatov/Wolf 2019
7144760 30340823 37485583 119 60040 20623 1.0457650931 1.0578359289 Raab 2020
39775736 275592497 315368233 182 218548 3469 1.0457625466 1.0527464522 Raab 2020
16545222 197273641 213818863 123 134514 76117 1.0445103314 1.0487427115 Raab 2020
34294350 94055281 128349631 97 353550 10981 1.0439655485 1.0604085140 Raab 2020
85968122 206916719 292884841 181 474962 308249 1.0437080792 1.0613402928 Raab 2020
16771540 57106657 73878197 137 122420 58937 1.0435528764 1.0576844880 Raab 2020
2972664 5323187 8295851 82 36252 30395 1.0427690852 1.0695379542 Raab 2020
18982866 16732321 35715187 129 147154 103919 1.0427244923 1.0834115109 Raab 2020
5609136 34016537 39625673 104 53934 38117 1.0412524005 1.0499075334 Kourbatov/Wolf 2019
260917668 36356059 297273727 198 1317766 776377 1.0403369145 1.1212483771 Raab 2020
47687280 54427211 102114491 115 414672 105179 1.0403195742 1.0726213426 Raab 2020
1153282126 40569031 1193851157 227 5080538 5005265 1.0393091300 1.1352839382 Raab 2020
22513392 345811177 368324569 198 113704 37313 1.0392757594 1.0425001861 Raab 2020
29611680 118797403 148409083 147 201440 149243 1.0388950704 1.0506756093 Raab 2020
26092110 69321059 95413169 165 158134 58367 1.0388234360 1.0559600795 Raab 2020
2413620 355417 2769037 53 45540 36637 1.0386945028 1.1428002353 Raab 2019
8160768 230301523 238462291 144 56672 43187 1.0384490461 1.0402329592 Raab 2020
30255160 1085694133 1115949293 166 182260 153573 1.0373558283 1.0386795991 Raab 2020
3422630 735473 4158103 115 29762 21185 1.0368176014 1.1281161479 Kourbatov/Wolf 2017
32799228 582134099 614933327 121 271068 151103 1.0363422342 1.0390636915 Raab 2020
24892056 204946981 229839037 189 131704 15557 1.0363200824 1.0422994383 Raab 2020
6415812 1693755359 1700171171 234 27418 8409 1.0360874064 1.0362451823 Raab 2020
11456256 1067601151 1079057407 192 59668 21295 1.0360534914 1.0365493807 Raab 2020
32356272 2058179 34414451 104 311118 191471 1.0360111463 1.1431414554 Raab 2020
40713186 90187127 130900313 177 230018 20071 1.0358686339 1.0553593797 Raab 2020
27299290 1237841221 1265140511 179 152510 70061 1.0358141038 1.0368533648 Raab 2020
17399370 440876999 458276369 159 109430 92959 1.0356890307 1.0376268994 Raab 2020
45020928 327791159 372812087 192 234484 217011 1.0356338254 1.0421886699 Raab 2020
25581952 76769131 102351083 176 145352 23275 1.0348088479 1.0501799186 Raab 2020
34372654 85955479 120328133 179 192026 119857 1.0341748708 1.0518985513 Raab 2020
984170 5357381 6341551 115 8558 73 1.0339720553 1.0443452341 Kourbatov/Wolf 2017
40743736 447004813 487748549 188 216722 124049 1.0335560254 1.0379415282 Raab 2020
45684090 94980541 140664631 97 470970 315571 1.0335532853 1.0538225485 Raab 2020
2266530 198565889 200832419 129 17570 7319 1.0335372951 1.0340700214 Kourbatov/Wolf 2017
7125388 5088100651 5095226039 251 28388 5859 1.0335068728 1.0335565879 Raab 2020
19609800 508010863 527620663 92 213150 74413 1.0334994824 1.0353716750 Raab 2020
53269880 58846181 112116061 142 375140 324341 1.0333898957 1.0660891427 Raab 2020
25371000 1138678631 1164049631 180 140950 84531 1.0330147550 1.0340650943 Raab 2020
42800280 98683987 141484267 97 441240 287467 1.0329970144 1.0516497002 Raab 2020
30754304 1077939353 1108693657 224 137296 28457 1.0329949635 1.0343472582 Raab 2020
46071424 1065488737 1111560161 224 205676 87057 1.0326385929 1.0346848669 Raab 2020
63992864 8219327 72212191 169 378656 267551 1.0323583994 1.1211359112 Raab 2020
41919540 260566829 302486369 130 322458 20765 1.0316370313 1.0392505301 Raab 2020
316790 726611 1043401 79 4010 801 1.0309808771 1.0553139996 Kourbatov/Wolf 2017
14359440 8356739 22716179 76 188940 43379 1.0302944159 1.0825626844 Raab 2019
32213400 314258017 346471417 159 202600 25417 1.0290886177 1.0340447422 Raab 2020
39621748 1392332203 1431953951 223 177676 63067 1.0283440350 1.0296738675 Raab 2020
16525824 233294389 249820213 159 103936 62005 1.0277069140 1.0312234078 Raab 2020
31984512 1415477209 1447461721 192 166586 162553 1.0272143510 1.0282661105 Raab 2020
31096700 113561549 144658249 145 214460 112209 1.0268341117 1.0394878515 Raab 2020
9220500 192977791 202198291 125 73764 11167 1.0267758273 1.0291722818 Raab 2020
13918926 697341727 711260653 177 78638 58581 1.0264518068 1.0273994434 Raab 2020
11171584 36676693 47848277 151 73984 54613 1.0261177143 1.0407929736 Raab 2020
7873524 78003593 85877117 114 69066 28079 1.0255655946 1.0307376110 Raab 2020
42573010 802434421 845007431 215 198014 81693 1.0252749170 1.0277884791 Raab 2020
6884640 618948611 625833251 180 38248 19475 1.0252706202 1.0257846030 Raab 2020
7661402 26493569 34154971 127 60326 10455 1.0250310223 1.0392788572 Raab 2020
63104964 348697267 411802231 186 339274 262869 1.0243014217 1.0326153144 Raab 2020
21623824 12534133 34157957 152 142262 15077 1.0238135041 1.0750502453 Raab 2020
411480 470669167 471080647 135 3048 55 1.0235488825 1.0235449993 Kourbatov/Wolf 2017
12749892 32656489 45406381 159 80188 19973 1.0230264286 1.0411095632 Raab 2020
22442616 201371617 223814233 189 118744 100537 1.0226532747 1.0280997629 Raab 2020
68916000 139171757 208087757 150 459440 420877 1.0223790546 1.0425614834 Raab 2020
2119706 665152001 667271707 211 10046 6341 1.0223668231 1.0224855590 Kourbatov/Wolf 2017
10272212 33203981 43476193 158 65014 46841 1.0216006404 1.0364862243 Raab 2020
94655398 250489231 345144629 191 495578 222341 1.0214682303 1.0373146802 Raab 2020
15522600 19386091 34908691 150 103484 34583 1.0209911728 1.0526772896 Raab 2020
21802200 139786609 161588809 150 145348 107181 1.0204493307 1.0279997768 Raab 2020
5910084 51763573 57673657 102 57942 21367 1.0199911211 1.0258795038 Kourbatov/Wolf 2019
15665628 140660603 156326231 121 129468 58355 1.0198122085 1.0253136814 Raab 2020
30813000 182792257 213605257 125 246504 132793 1.0195126958 1.0274957358 Raab 2020
33604510 154856431 188460941 185 181646 94039 1.0190978591 1.0292143015 Raab 2020
31293030 908258651 939551681 145 215814 113339 1.0190659650 1.0206839169 Raab 2020
50925936 58094497 109020433 113 450672 408481 1.0189432476 1.0504748177 Raab 2020
62891296 1051239697 1114130993 221 284576 15953 1.0186773964 1.0214538133 Raab 2020
13832418 724565069 738397487 201 68818 49165 1.0182064728 1.0191040049 Raab 2020
56777754 267504733 324282487 113 502458 197077 1.0181853448 1.0278000222 Raab 2020
657504 896016139 896673643 144 4566 2563 1.0179389550 1.0179401694 Kourbatov/Wolf 2017
46246642 108866971 155113613 167 276926 35053 1.0173754306 1.0354406993 Raab 2020
42567198 733564303 776131501 213 199846 129483 1.0166825429 1.0194136059 Raab 2020
7326222 222677837 230004059 183 40034 8729 1.0166221904 1.0182458794 Kourbatov/Wolf 2019
2823288 37906669 40729957 156 18098 9457 1.0162761199 1.0202123198 Kourbatov/Wolf 2017
3185830 8337054667 8340240497 265 12022 2041 1.0157579142 1.0157635451 Raab 2020
3923892 3025085407 3029009299 207 18956 11103 1.0148968246 1.0149380057 Raab 2020
229350 1409633 1638983 55 4170 173 1.0145547849 1.0239918076 Kourbatov/Wolf 2017
5450496 366870073 372320569 192 28388 11949 1.0140771094 1.0147754528 Kourbatov/Wolf 2019
75525164 233697383 309222547 157 481052 387163 1.0140279077 1.0278960790 Raab 2020
9639760 111124171 120763931 155 62192 49259 1.0138334837 1.0181940452 Raab 2020
30930676 24205417 55136093 161 192116 190917 1.0134223607 1.0550102605 Raab 2020
50418420 386155171 436573591 195 258556 131063 1.0133228991 1.0193961624 Raab 2020
40721638 52043323 92764961 163 249826 79515 1.0128376956 1.0421613643 Raab 2020
47941560 49222847 97164407 86 557460 166367 1.0125803645 1.0463002847 Raab 2020
37405620 150807611 188213231 98 381690 40061 1.0125794282 1.0238363687 Raab 2020
28110280 23247661 51357941 116 242330 226311 1.0124632857 1.0526838429 Raab 2020
21274558 1705015261 1726289819 229 92902 77757 1.0124436726 1.0130055229 Raab 2020
37123944 103922617 141046561 156 237974 165953 1.0122190047 1.0278829102 Raab 2020
385368674 25348859 410717533 199 1936526 174021 1.0117855356 1.1024959563 Raab 2020
7623726 160872571 168496297 121 63006 18253 1.0117585015 1.0141160813 Raab 2020
19392048 104769641 124161689 108 179556 88493 1.0114121155 1.0202565037 Raab 2020
17191872 931742089 948933961 144 119388 38137 1.0111387167 1.0119911112 Raab 2020
2453760 11626561 14080321 135 18176 12097 1.0107626289 1.0218791350 Kourbatov/Wolf 2017
43248460 98697649 141946109 139 311140 66269 1.0107319907 1.0291933253 Raab 2020
3002682 8462609 11465291 89 33738 28109 1.0107025944 1.0283717872 Kourbatov/Wolf 2017
20830992 285015677 305846669 156 133532 58389 1.0104842645 1.0140172971 Raab 2020
37745708 153693563 191439271 143 263956 71171 1.0104329056 1.0215972900 Raab 2020
1906050 4223927657 4225833707 131 14550 4457 1.0103872954 1.0103918943 Raab 2020
56444996 994774373 1051219369 218 258922 254971 1.0103744227 1.0129958216 Raab 2020
2937868 71725099 74662967 166 17698 12803 1.0103309882 1.0124218941 Kourbatov/Wolf 2017
3108778 524646211 527754989 199 15622 12585 1.0098218219 1.0100720665 Kourbatov/Wolf 2017
34340500 966299149 1000639649 173 198500 1149 1.0095741809 1.0112252851 Raab 2020
27316160 26855831 54171991 160 170726 51849 1.0091149620 1.0450432633 Raab 2020
38244528 216529571 254774099 126 303528 114107 1.0090204027 1.0171962322 Raab 2020
21688044 406051133 427739177 107 202692 59057 1.0087753617 1.0113243560 Raab 2020
25745040 747766631 773511671 162 158920 48031 1.0087685990 1.0103823236 Raab 2020
25988580 496424063 522412643 102 254790 93143 1.0087199699 1.0111970717 Raab 2020
46009194 501206653 547215847 159 289366 24741 1.0086176344 1.0128998671 Raab 2020
47736960 152530297 200267257 115 415104 187129 1.0085751202 1.0222599621 Raab 2020
15447230 354861707 370308937 157 98390 67367 1.0084080795 1.0105063318 Raab 2020
532602 355339 887941 63 8454 271 1.0081862161 1.0661281933 Kourbatov/Wolf 2017
13705524 244179227 257884751 126 108774 90371 1.0078434403 1.0105783718 Raab 2020
20039880 715497919 735537799 140 143142 74203 1.0076771137 1.0089878396 Raab 2020
40088160 132866873 172955033 82 488880 380393 1.0074523194 1.0207507645 Raab 2020
58811344 820178353 878989697 212 277412 148481 1.0074489688 1.0107563320 Raab 2020
16594812 285872417 302467229 118 140634 104129 1.0073862785 1.0101922452 Raab 2020
7913376 366478501 374391877 129 61344 9445 1.0072590496 1.0082840851 Raab 2020
6336090 10862323 17198413 135 46934 20569 1.0064940453 1.0322635782 Kourbatov/Wolf 2019
1263426 10176791 11440217 129 9794 825 1.0056800570 1.0124473202 Kourbatov/Wolf 2017
46050228 217133753 263183981 189 243652 39821 1.0055799493 1.0152019122 Raab 2020
48286400 476773643 525060043 160 301790 247233 1.0053022416 1.0099987903 Raab 2020
91995972 134314139 226310111 186 494602 276997 1.0051970084 1.0304647697 Raab 2020
7044864 302145839 309190703 128 55038 42257 1.0048671503 1.0059802504 Kourbatov/Wolf 2019
59879754 195127693 255007447 171 350174 80775 1.0047355186 1.0180212879 Raab 2020
6580070 9659921 16239991 115 57218 47297 1.0046426332 1.0335781556 Kourbatov/Wolf 2019
51467746 27521653 78989399 151 340846 253973 1.0046376418 1.0546436448 Raab 2020
43509780 145858093 189367873 94 462870 54043 1.0045802322 1.0176743975 Raab 2020
1717149024 2144897 1719293921 144 11924646 2144897 1.0045650866 1.1079281784 Raab 2020
13075056 1108727 14183783 87 150288 56711 1.0044797434 1.1084765832 Raab 2020
13439592 1168184821 1181624413 146 92052 44941 1.0040622170 1.0045775514 Raab 2020
28352916 35142521 63495437 162 175018 138921 1.0037465003 1.0340546108 Raab 2020
21976512 549084871 571061383 204 107728 102983 1.0037234187 1.0056145476 Raab 2020
29832516 238445833 268278349 189 157844 101393 1.0036031644 1.0095146956 Raab 2020
36180210 145871087 182051297 165 219274 53877 1.0035484669 1.0147724824 Raab 2020
40408416 986864401 1027272817 216 187076 38501 1.0033433424 1.0052328333 Raab 2020
33483000 215811593 249294593 150 223220 181073 1.0032754840 1.0105108305 Raab 2020
4358676 456043963 460402639 133 32772 21583 1.0031136169 1.0035397670 Raab 2020
31133600 439349837 470483437 200 155668 54741 1.0031057406 1.0064506471 Raab 2020
27551940 338556937 366108877 195 141292 21305 1.0030711445 1.0069378649 Raab 2020
15331396 565558423 580889819 202 75898 42425 1.0029708311 1.0042463480 Raab 2020
23412288 175749583 199161871 183 127936 93455 1.0027528576 1.0091045460 Raab 2020
1594416 145465687 147060103 118 13512 9007 1.0026889378 1.0031790166 Kourbatov/Wolf 2017
10861720 838264771 849126491 164 66230 57891 1.0024939750 1.0030815954 Raab 2020
2306938 82541821 84848759 167 13814 3171 1.0022590147 1.0036450169 Kourbatov/Wolf 2017
62453988 21427013 83881001 153 408196 200821 1.0022380684 1.0635856005 Raab 2020
17885700 1540935449 1558821149 153 116900 76549 1.0019820978 1.0024980415 Raab 2020
20569432 769650307 790219739 194 106028 99083 1.0018790832 1.0031212916 Raab 2020
39889386 27538787 67428173 107 372798 324533 1.0017029036 1.0452937817 Raab 2020
12379428 663185953 675565381 138 89706 79201 1.0016346146 1.0024974574 Raab 2020
24229590 583703311 607932901 165 146846 137307 1.0015954952 1.0035453014 Raab 2020
43562550 1901563 45464113 83 524850 327013 1.0014031914 1.1083793957 Raab 2020
20149566 393144877 413294443 127 158658 149011 1.0013961710 1.0038325361 Raab 2020
12923460 84117277 97040737 110 117486 114787 1.0013287456 1.0087976608 Raab 2020
54264 825353008489 ...062753 357 152 33 1.0010143609 1.0010132538 Raab 2020
47797860 29115551 76913411 110 434526 2309 1.0008633483 1.0472594243 Raab 2020
25487000 313905113 339392113 140 182050 50913 1.0008612832 1.0047158319 Raab 2020
19510266 489350311 508860577 201 97066 40605 1.0002453898 1.0021310501 Raab 2020
26869948 20920033 47789981 134 200522 65745 1.0000761994 1.0415155353 Raab 2020
1885228 163504573 165389801 179 10532 5805 1.0000704209 1.0005917231 Kourbatov/Wolf 2017
3758772 144803717 148562489 118 31854 27287 1.0000152764 1.0012763548 Kourbatov/Wolf 2017
Next goal: CSG > A201559 |
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2020-06-10, 15:11
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#20 |
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Dec 2008
you know...around...
2×11×29 Posts |
Mind the gap!
A killing sieve at work:
Code:
g = 99,754,416 p = 397,778,383 q = 615,768 = 2³ × 3 × 25,657 phi(q) = 205,248 k = 162 g / [phi(q) log²(p')] = 1.21199459979... Sum Ri'(x) method = 1.2250203518... Merit = 24.40047328... (2020-06-10) 397778383 = 397778383 398394151 = 293 x 773 x 1759 399009919 = 7 x 11 x 5181947 399625687 = 79 x 461 x 10973 400241455 = 5 x 17 x 89 x 191 x 277 400857223 = 13 x 37 x 43 x 19381 401472991 = 10331 x 38861 402088759 = 61 x 6591619 402704527 = 29 x 13886363 403320295 = 5 x 7 x 23 x 501019 403936063 = 3709 x 108907 404551831 = 389 x 1039979 405167599 = 10987 x 36877 405783367 = 11 x 3491 x 10567 406399135 = 5 x 151 x 193 x 2789 407014903 = 19 x 31 x 103 x 6709 407630671 = 7 x 47 x 1238999 408246439 = 53 x 7702763 408862207 = 13 x 13 x 67 x 36109 409477975 = 5 x 5 x 16379119 410093743 = 149 x 2752307 410709511 = 17 x 71 x 227 x 1499 411325279 = 6899 x 59621 411941047 = 7 x 557 x 105653 412556815 = 5 x 11 x 7501033 413172583 = 887 x 465809 413788351 = 12239 x 33809 414404119 = 373 x 709 x 1567 415019887 = 317 x 1309211 415635655 = 5 x 41 x 41 x 49451 416251423 = 7 x 7 x 7 x 1213561 416867191 = 13 x 32066707 417482959 = 23 x 18151433 418098727 = 263 x 761 x 2089 418714495 = 5 x 19 x 73 x 173 x 349 419330263 = 11 x 38120933 419946031 = 11981 x 35051 420561799 = 7 x 29 x 2071733 421177567 = 17 x 487 x 50873 421793335 = 5 x 4643 x 18169 422409103 = 7607 x 55529 423024871 = 9497 x 44543 423640639 = 37 x 11449747 424256407 = 457 x 928351 424872175 = 5 x 5 x 7 x 13 x 186757 425487943 = 839 x 507137 426103711 = 11 x 31 x 197 x 6343 426719479 = 5881 x 72559 427335247 = 43 x 1889 x 5261 427951015 = 5 x 409 x 209267 428566783 = 1487 x 288209 429182551 = 7 x 4861 x 12613 429798319 = 83 x 257 x 20149 430414087 = 19 x 157 x 144289 431029855 = 5 x 331 x 260441 431645623 = 17 x 23 x 401 x 2753 432261391 = 97 x 127 x 35089 432877159 = 11 x 13 x 59 x 51307 433492927 = 7 x 61927561 434108695 = 5 x 86821739 434724463 = 17929 x 24247 435340231 = 241 x 829 x 2179 435955999 = 1861 x 234259 436571767 = 47 x 719 x 12919 437187535 = 5 x 87437507 437803303 = 7 x 2579 x 24251 438419071 = 29 x 15117899 439034839 = 7013 x 62603 439650607 = 11 x 61 x 643 x 1019 440266375 = 5 x 5 x 5 x 3522131 440882143 = 13 x 41 x 53 x 15607 441497911 = 569 x 775919 442113679 = 7 x 17 x 19 x 195539 442729447 = 1129 x 392143 443345215 = 5 x 7919 x 11197 443960983 = 167 x 2658449 444576751 = 179 x 2483669 445192519 = 31 x 14361049 445808287 = 23 x 991 x 19559 446424055 = 5 x 7 x 7 x 11 x 11 x 11 x 37 x 37 447039823 = 1201 x 372223 447655591 = 1367 x 327473 448271359 = 79 x 397 x 14293 448887127 = 13 x 101 x 341879 449502895 = 5 x 593 x 151603 450118663 = 67 x 113 x 59453 450734431 = 7 x 64390633 451350199 = 137 x 3294527 451965967 = 107 x 4223981 452581735 = 5 x 17 x 5324491 453197503 = 11 x 41199773 453813271 = 19 x 43 x 251 x 2213 454429039 = 71 x 859 x 7451 455044807 = 7 x 89 x 109 x 6701 455660575 = 5 x 5 x 131 x 139133 456276343 = 29 x 15733667 456892111 = 13 x 35145547 457507879 = 229 x 1997851 458123647 = 21317 x 21491 458739415 = 5 x 2383 x 38501 459355183 = 7 x 367 x 178807 459970951 = 11 x 23 x 1818067 460586719 = 13367 x 34457 461202487 = 19319 x 23873 461818255 = 5 x 2749 x 33599 462434023 = 14447 x 32009 463049791 = 17 x 27238223 463665559 = 7 x 73 x 907369 464281327 = 31 x 1483 x 10099 464897095 = 5 x 13 x 7152263 465512863 = 19 x 47 x 547 x 953 466128631 = 41 x 239 x 47569 466744399 = 11 x 1867 x 22727 467360167 = 12409 x 37663 467975935 = 5 x 7 x 379 x 35279 468591703 = 4349 x 107747 469207471 = 37 x 59 x 59 x 3643 469823239 = 6619 x 70981 470439007 = 103 x 4567369 471054775 = 5 x 5 x 18842191 471670543 = 9371 x 50333 472286311 = 7 x 67469473 472902079 = 13 x 877 x 41479 473517847 = 11 x 17 x 53 x 47777 474133615 = 5 x 23 x 29 x 142169 474749383 = 223 x 233 x 9137 475365151 = 2819 x 168629 475980919 = 14411 x 33029 476596687 = 7 x 7 x 9726463 477212455 = 5 x 19 x 61 x 82349 477828223 = 3001 x 159223 478443991 = 1489 x 321319 479059759 = 181 x 281 x 9419 479675527 = 307 x 443 x 3527 480291295 = 5 x 11 x 43 x 311 x 653 480907063 = 7 x 13 x 83 x 63671 481522831 = 8387 x 57413 482138599 = 613 x 757 x 1039 482754367 = 139 x 3473053 483370135 = 5 x 31 x 269 x 11593 483985903 = 17 x 28469759 484601671 = 20963 x 23117 485217439 = 7 x 971 x 71387 485833207 = 491 x 989477 486448975 = 5 x 5 x 19457959 487064743 = 11 x 44278613 487680511 = 13001 x 37511 488296279 = 23 x 21230273 488912047 = 13 x 19 x 19 x 104179 489527815 = 5 x 7 x 13986509 490143583 = 11551 x 42433 490759351 = 10891 x 45061 491375119 = 41 x 67 x 178877 491990887 = 29 x 29 x 37 x 97 x 163 492606655 = 5 x 2971 x 33161 493222423 = 7841 x 62903 493838191 = 7 x 11 x 6413483 494453959 = 17 x 47 x 618841 495069727 = 2267 x 218381 495685495 = 5 x 99137099 496301263 = 7559 x 65657 496917031 = 13 x 79 x 483853 497532799 = 497532799 |
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2020-06-19, 16:57
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#21 |
May 2018
22·53 Posts |
Is this gap the largest CSG known for a prime gap in residues?
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2020-06-19, 19:12
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#22 |
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Dec 2008
you know...around...
2·11·29 Posts |
As far as I know, it is.
I'm not aware of any gap with a larger CSG value. |
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