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2007-06-23, 22:11   #1
gd_barnes

May 2007
Kansas; USA

72·11·19 Posts
List of most small twins of form k*2^n+/-1

To whom may be interested,

I went through an excercise to find an easy way to get most of the primes of the form k * 2 ^ n +/- 1 with small values of k. What I did was I extracted all of the k's and n's from the RPS site, the Primesearch site, and the Proth search site into Excel spreadsheets. I then used Excel formulas to match up primes for the -1 sites (RPS and Primesearch) to the +1 site (Proth). The largest value of k that I could use was 599 because that is the highest that the Proth search site goes to.

Attached is a Notepad file that shows what I came up with. The first part is sorted by n. The second part by k.

Although the largest twins that I found don't come close to the top 10 or 20 twins, I think it's good to have comprehensive lists like this as 'building blocks' for future searches.

The largest twins that I found from the effort are:
1. 459 * 2 ^ 8529 +/- 1
2. 291 * 2 ^ 1553 +/- 1
3. 177 * 2 ^ 1032 +/- 1

Not too bad considering I could only match up to k=599. Obviously this list is constrainted by the lower limits of how far each k has been searched for BOTH Riesel primes and Proth primes.

If anyone knows of a more comprehensive list of Proth primes (i.e. of the form k * 2^n + 1) where k > 600 like we have at RPS for Rielsel primes, I'll extend this effort to include more k's.

Gary
Attached Files
 twin primes match.txt (3.7 KB, 381 views)

 2007-06-24, 05:56 #2 Citrix     Jun 2003 32·52·7 Posts Here are twins from k=1 to 10145 (used this limit as LLR is faster for these k's) and corresponding twin n's upto n=250. Would like to extend these further, anyone want to help. I think k=1-300 have been searched enough. Code: 3 1 3 2 3 6 3 18 9 1 9 3 9 7 9 43 9 63 9 211 15 1 15 2 15 4 15 10 21 1 21 7 27 2 27 4 33 6 33 22 39 3 45 2 45 9 45 14 45 29 45 189 51 1 51 9 57 2 57 8 57 10 63 14 69 1 69 19 75 1 75 3 75 6 75 43 81 5 81 21 81 27 87 2 87 8 93 4 93 10 99 1 99 5 99 11 99 65 105 2 105 5 105 8 105 155 117 4 117 6 117 16 129 3 129 5 129 59 135 1 135 10 135 238 141 1 141 7 141 61 147 44 147 60 165 2 165 3 165 5 165 12 165 39 165 84 177 12 177 48 195 4 195 8 195 14 201 3 201 9 207 2 213 36 213 80 231 1 231 7 243 12 243 18 243 24 255 2 255 41 261 1 261 3 261 9 267 4 267 34 267 40 273 2 273 10 285 1 297 14 309 1 309 143 315 22 315 72 321 1 321 5 327 4 333 54 339 3 339 11 345 4 345 15 345 30 345 40 345 150 357 2 357 10 357 14 363 2 369 13 375 3 375 14 375 26 375 33 381 17 381 21 387 28 387 88 399 11 405 1 405 2 405 46 405 80 411 1 411 19 417 2 417 8 417 62 423 8 429 1 429 9 429 37 435 4 441 1 441 3 441 13 441 181 447 2 447 20 453 48 459 3 459 9 465 6 465 9 471 3 483 2 483 18 483 22 489 5 495 16 495 33 507 2 507 26 513 6 513 12 519 11 519 55 525 1 525 6 525 8 525 26 525 190 531 1 537 6 537 102 549 11 555 9 555 27 561 7 567 2 585 2 585 32 585 57 591 5 597 70 603 10 603 76 609 19 615 1 615 14 621 3 627 6 633 32 639 1 639 13 645 1 645 5 645 7 651 1 657 58 663 24 669 11 675 5 675 9 675 15 675 26 681 31 687 34 699 5 699 125 705 3 705 6 711 17 717 12 723 6 723 16 735 3 735 20 735 21 741 1 741 7 741 11 741 35 747 6 759 17 765 4 765 10 765 12 765 18 765 22 765 25 765 168 777 10 795 3 813 2 813 4 813 58 819 3 819 63 825 2 831 9 843 2 843 20 849 1 849 3 849 45 849 91 855 4 855 10 855 11 861 1 861 25 867 2 867 8 879 17 885 2 885 14 885 17 891 3 897 28 903 4 903 6 915 22 915 25 915 55 915 70 921 15 927 50 933 40 939 1 945 3 945 8 945 12 951 13 957 22 963 2 975 1 975 24 975 37 981 5 993 4 993 8 993 14 999 1 999 13 1005 2 1011 3 1017 12 1023 2 1023 242 1029 3 1029 7 1035 8 1035 14 1041 1 1053 14 1065 1 1065 2 1065 28 1065 56 1071 1 1071 7 1071 25 1089 5 1089 15 1089 131 1095 9 1095 42 1101 37 1107 50 1119 1 1119 13 1125 3 1125 51 1125 58 1125 63 1125 123 1131 15 1137 2 1143 4 1155 1 1155 3 1155 18 1155 31 1179 3 1179 11 1179 23 1179 51 1179 141 1185 25 1191 1 1191 61 1197 2 1197 10 1197 16 1197 52 1197 70 1197 206 1203 104 1209 9 1215 3 1221 3 1233 2 1233 16 1245 5 1251 3 1257 6 1263 6 1269 37 1275 1 1275 2 1275 31 1281 17 1281 23 1287 8 1299 11 1305 5 1305 32 1323 106 1329 1 1329 65 1335 15 1347 12 1353 4 1365 1 1365 4 1365 12 1365 39 1383 176 1389 21 1395 1 1395 3 1395 7 1395 21 1395 43 1401 1 1401 17 1401 37 1407 12 1413 2 1419 3 1419 15 1419 147 1431 23 1437 6 1443 8 1455 16 1455 85 1455 133 1467 2 1467 6 1467 14 1467 92 1479 3 1479 19 1485 1 1485 17 1485 58 1491 5 1491 17 1491 29 1491 47 1497 122 1509 3 1509 21 1509 125 1515 5 1515 105 1527 16 1527 20 1533 2 1539 7 1545 10 1545 34 1545 82 1551 9 1551 33 1575 2 1575 6 1575 13 1575 16 1575 20 1581 5 1587 76 1593 26 1599 9 1605 12 1611 19 1617 10 1617 20 1623 22 1623 52 1623 64 1629 1 1629 7 1629 13 1629 87 1635 11 1641 11 1659 5 1665 1 1665 2 1665 5 1665 25 1677 14 1695 1 1695 2 1695 46 1707 2 1713 4 1719 33 1725 23 1725 26 1731 1 1731 39 1737 2 1737 4 1743 14 1743 28 1755 204 1761 17 1767 50 1779 1 1785 30 1791 1 1791 7 1797 4 1803 2 1809 15 1815 16 1827 2 1827 6 1833 2 1833 16 1863 20 1863 32 1869 7 1869 17 1869 23 1869 47 1875 17 1881 15 1881 169 1887 2 1887 12 1887 62 1893 8 1899 19 1911 1 1911 3 1911 5 1911 41 1923 22 1935 8 1935 12 1935 188 1941 49 1941 175 1947 4 1953 4 1959 1 1959 7 1959 49 1965 1 1965 10 1983 4 1983 124 1989 5 1995 5 1995 6 1995 14 1995 16 1995 21 1995 26 1995 39 2001 1 2001 19 2001 29 2001 53 2013 6 2025 1 2037 6 2055 2 2055 20 2061 9 2061 35 2067 4 2067 12 2067 22 2073 2 2079 1 2079 3 2079 31 2079 81 2079 103 2091 7 2097 2 2097 14 2097 36 2103 6 2109 1 2115 1 2115 14 2115 173 2121 1 2121 163 2127 4 2127 22 2127 50 2133 4 2133 58 2139 5 2151 3 2151 15 2157 2 2157 4 2157 124 2163 16 2163 20 2163 60 2169 1 2175 6 2175 43 2175 111 2181 29 2181 33 2181 131 2187 6 2187 30 2187 36 2205 2 2205 4 2205 7 2205 19 2205 40 2205 110 2211 1 2211 7 2211 19 2211 49 2217 12 2229 5 2241 1 2241 5 2241 13 2253 2 2253 20 2259 1 2265 3 2265 81 2271 5 2271 9 2271 45 2277 10 2277 178 2283 4 2289 3 2289 9 2289 11 2295 14 2295 47 2313 14 2319 1 2319 7 2319 61 2325 1 2325 4 2331 21 2343 30 2349 5 2355 2 2355 12 2355 32 2361 1 2361 25 2373 36 2385 3 2385 6 2385 22 2397 6 2403 4 2403 52 2409 11 2415 9 2415 10 2415 54 2433 32 2445 15 2457 46 2457 74 2463 16 2469 3 2469 7 2469 67 2487 6 2487 12 2487 18 2493 184 2499 3 2499 17 2499 21 2505 1 2511 1 2517 2 2517 62 2523 2 2523 20 2529 3 2535 2 2535 53 2547 10 2547 14 2553 4 2565 126 2571 21 2571 231 2577 4 2577 76 2583 2 2583 6 2595 4 2595 7 2595 46 2601 3 2601 5 2607 2 2607 6 2607 20 2613 24 2625 2 2625 21 2625 31 2631 7 2649 3 2655 7 2655 49 2661 19 2673 8 2673 116 2679 49 2685 9 2685 54 2691 5 2691 9 2697 10 2697 12 2697 28 2697 78 2703 14 2703 16 2709 1 2709 19 2715 2 2715 13 2721 1 2721 105 2733 48 2739 1 2739 9 2739 13 2745 7 2751 1 2757 40 2769 5 2769 33 2775 5 2781 7 2787 14 2793 2 2805 15 2805 27 2811 15 2817 6 2829 1 2829 5 2835 63 2847 172 2859 17 2865 30 2871 1 2889 7 2895 5 2895 8 2895 11 2895 51 2913 26 2919 35 2925 1 2925 2 2925 13 2925 37 2925 67 2937 44 2943 20 2955 5 2955 7 2961 3 2961 7 2961 17 2967 10 2967 16 2979 3 2985 2 2985 14 2985 66 2997 10 2997 50 3003 6 3015 16 3027 2 3027 18 3039 11 3045 1 3045 22 3057 18 3057 52 3063 2 3063 44 3069 11 3075 4 3081 7 3081 73 3087 4 3087 6 3087 112 3093 10 3093 38 3099 1 3105 8 3105 134 3111 27 3111 41 3117 6 3117 132 3123 34 3129 3 3129 15 3135 1 3135 2 3135 44 3135 74 3153 2 3153 14 3153 30 3165 5 3165 10 3165 20 3183 12 3189 9 3195 17 3213 16 3213 56 3219 7 3219 29 3225 1 3225 3 3225 13 3231 3 3231 5 3231 15 3243 12 3243 16 3249 5 3249 29 3249 41 3255 11 3255 32 3273 24 3273 60 3285 1 3285 7 3285 57 3303 118 3315 21 3315 27 3321 89 3327 4 3339 3 3339 13 3339 37 3339 93 3345 1 3351 1 3351 9 3363 8 3369 3 3369 9 3369 15 3375 10 3375 26 3381 1 3381 5 3399 11 3399 15 3399 23 3399 33 3399 57 3405 3 3405 5 3405 8 3405 27 3405 227 3417 16 3423 2 3429 61 3435 1 3435 3 3435 33 3441 3 3441 15 3447 20 3453 42 3465 4 3465 5 3465 10 3465 14 3465 24 3465 35 3465 80 3471 7 3477 4 3477 12 3477 24 3477 52 3483 2 3489 35 3495 6 3495 28 3507 10 3507 46 3513 4 3513 70 3519 13 3525 9 3525 44 3537 10 3549 19 3555 5 3555 16 3555 137 3579 15 3591 7 3591 63 3591 77 3597 2 3603 34 3615 212 3627 14 3633 14 3633 54 3639 41 3651 3 3651 111 3657 2 3663 22 3663 78 3669 25 3675 1 3675 3 3675 12 3675 29 3675 36 3681 79 3693 20 3699 23 3705 15 3717 2 3717 4 3717 16 3717 164 3729 1 3735 3 3741 153 3747 94 3765 8 3765 10 3765 35 3771 7 3777 20 3783 36 3789 9 3795 1 3795 5 3795 52 3801 5 3813 30 3819 5 3825 5 3825 11 3837 8 3849 7 3855 3 3855 33 3861 5 3867 38 3879 1 3879 11 3879 29 3879 35 3885 3 3885 6 3885 7 3885 8 3885 20 3909 9 3915 3 3915 123 3915 147 3927 10 3933 2 3933 4 3933 10 3933 14 3939 1 3939 3 3957 4 3957 120 3963 10 3963 38 3969 11 3975 1 3975 4 3981 3 3981 13 3981 61 3993 2 3993 12 4005 1 4005 8 4011 11 4011 27 4011 51 4017 2 4017 16 4029 23 4029 29 4035 2 4035 5 4035 8 4035 23 4035 60 4035 62 4047 2 4059 7 4059 25 4059 31 4059 241 4065 12 4077 12 4089 35 4089 83 4095 4 4095 18 4095 125 4107 100 4113 2 4119 9 4125 27 4125 87 4131 49 4137 82 4143 140 4155 56 4155 174 4161 3 4161 75 4167 6 4173 2 4173 10 4173 32 4185 14 4191 7 4209 9 4215 1 4215 106 4221 3 4221 11 4221 35 4239 5 4245 2 4245 198 4257 2 4257 4 4263 4 4269 1 4275 10 4275 39 4281 5 4287 180 4299 1 4299 125 4305 4 4305 16 4311 11 4311 77 4323 2 4323 6 4323 8 4323 12 4323 36 4329 15 4347 2 4347 6 4347 8 4353 10 4359 81 4365 51 4383 14 4389 17 4395 2 4407 20 4419 1 4431 1 4431 3 4437 2 4449 3 4449 29 4449 39 4449 53 4455 6 4461 13 4467 4 4467 124 4467 128 4473 26 4473 76 4473 92 4485 1 4485 28 4497 2 4497 68 4497 152 4509 7 4515 2 4515 5 4515 19 4521 1 4521 7 4521 29 4527 24 4527 58 4533 2 4533 8 4545 13 4557 6 4563 2 4569 27 4575 8 4575 9 4575 104 4599 3 4599 19 4605 4 4605 10 4611 15 4623 6 4635 2 4635 4 4641 1 4647 8 4671 1 4677 10 4695 7 4695 10 4713 132 4719 1 4719 5 4725 35 4731 1 4731 83 4743 6 4749 3 4749 5 4749 11 4749 35 4749 41 4755 4 4761 11 4761 17 4767 42 4773 4 4773 64 4785 2 4785 47 4791 3 4791 15 4803 2 4803 10 4803 32 4809 5 4815 1 4815 5 4821 3 4821 13 4821 49 4827 6 4833 6 4839 1 4839 3 4845 2 4845 7 4851 9 4857 2 4857 4 4857 8 4857 22 4857 32 4857 58 4863 22 4869 141 4887 4 4893 6 4899 7 4905 3 4905 19 4929 1 4929 79 4935 7 4935 12 4935 14 4935 16 4935 17 4947 4 4947 28 4953 14 4965 1 4965 37 4977 4 4977 8 4995 6 5001 5 5001 11 5013 4 5013 10 5019 1 5019 3 5019 19 5019 45 5025 20 5025 125 5031 19 5037 2 5043 8 5043 14 5049 7 5055 10 5055 40 5055 68 5061 23 5073 12 5079 5 5091 7 5097 4 5103 4 5115 9 5115 30 5115 58 5127 2 5127 6 5127 12 5133 6 5139 5 5139 17 5145 39 5145 48 5151 1 5151 41 5163 6 5163 116 5187 2 5187 20 5193 2 5193 44 5205 47 5229 1 5229 77 5241 15 5247 6 5253 2 5259 3 5259 69 5259 153 5265 1 5265 2 5271 41 5277 10 5283 168 5295 14 5295 50 5301 3 5325 4 5331 11 5343 6 5343 28 5343 36 5349 5 5355 1 5355 3 5373 2 5379 9 5385 9 5385 39 5385 40 5385 57 5397 2 5397 4 5397 14 5403 2 5403 16 5415 3 5415 6 5433 4 5433 14 5439 5 5445 1 5445 4 5445 8 5451 3 5451 7 5451 27 5451 33 5469 1 5469 13 5475 13 5475 25 5475 103 5481 5 5481 11 5481 185 5493 34 5499 11 5505 5 5505 57 5505 80 5511 3 5511 21 5523 2 5523 6 5523 32 5529 1 5529 205 5535 1 5535 3 5535 7 5535 48 5535 78 5541 9 5547 6 5553 16 5559 1 5559 5 5559 11 5565 7 5565 13 5565 14 5565 119 5571 29 5577 6 5583 8 5589 99 5595 4 5595 30 5607 14 5607 24 5625 5 5625 69 5643 2 5643 38 5649 9 5649 23 5655 2 5655 19 5655 44 5661 51 5679 9 5679 13 5685 2 5685 8 5697 4 5697 76 5709 15 5715 2 5715 14 5715 149 5727 14 5727 26 5733 16 5745 1 5745 10 5757 2 5757 12 5769 5 5775 1 5775 4 5775 7 5775 19 5781 7 5787 12 5787 48 5793 84 5799 5 5805 3 5805 18 5805 84 5823 2 5835 3 5835 9 5835 27 5835 45 5835 129 5847 22 5859 1 5859 27 5859 31 5859 81 5859 215 5865 7 5865 26 5865 50 5871 25 5889 1 5901 5 5907 2 5919 3 5925 15 5925 35 5943 4 5943 10 5949 5 5949 11 5955 7 5955 16 5961 117 5967 8 5985 1 6015 3 6015 13 6015 36 6021 1 6021 25 6027 2 6027 12 6027 42 6033 20 6033 32 6033 38 6039 3 6039 39 6045 2 6045 8 6051 3 6057 22 6063 20 6063 40 6063 130 6069 9 6081 1 6081 3 6087 6 6093 2 6093 12 6099 19 6105 2 6105 10 6105 16 6105 17 6105 46 6105 80 6117 56 6123 24 6129 3 6129 135 6147 50 6159 7 6165 4 6165 34 6171 3 6177 20 6183 4 6183 82 6189 1 6195 20 6195 26 6195 57 6195 92 6201 19 6207 54 6225 7 6231 7 6231 79 6237 46 6249 3 6249 13 6249 37 6249 63 6273 8 6273 10 6273 16 6279 5 6279 33 6285 5 6285 56 6297 14 6321 41 6327 2 6327 80 6333 24 6333 54 6345 20 6351 99 6369 5 6375 4 6375 13 6375 18 6381 9 6393 18 6405 3 6411 1 6417 34 6435 3 6435 36 6441 17 6459 1 6465 3 6465 14 6471 3 6477 22 6483 2 6489 9 6501 1 6501 45 6501 175 6531 5 6531 13 6549 5 6549 9 6549 15 6549 59 6555 11 6555 21 6555 162 6555 221 6561 33 6561 43 6567 116 6573 12 6573 22 6579 7 6585 4 6585 52 6591 5 6609 1 6615 217 6627 4 6627 12 6627 18 6639 95 6645 4 6645 6 6645 9 6645 37 6669 1 6669 21 6675 2 6675 15 6675 51 6687 6 6693 80 6699 1 6699 3 6705 5 6705 7 6705 10 6705 25 6711 19 6717 6 6717 12 6723 2 6729 61 6735 34 6765 2 6765 6 6765 30 6771 19 6777 2 6783 6 6783 12 6783 60 6795 19 6795 45 6807 6 6807 8 6825 4 6825 30 6825 42 6825 60 6831 23 6831 29 6837 10 6843 44 6855 1 6861 1 6879 1 6885 2 6891 5 6897 10 6897 108 6903 142 6915 1 6915 31 6915 37 6927 14 6927 56 6939 1 6945 4 6945 7 6951 1 6951 9 6957 20 6963 6 6963 12 6963 16 6969 5 6975 6 6975 11 6975 12 6975 59 6975 74 6981 27 6981 205 6987 28 6999 1 6999 41 7005 1 7005 3 7023 24 7023 64 7029 23 7029 35 7029 71 7035 8 7035 48 7035 122 7041 1 7041 7 7059 9 7059 11 7059 23 7065 4 7065 6 7065 39 7065 66 7071 25 7077 2 7083 4 7083 28 7089 3 7089 7 7095 17 7095 30 7101 3 7101 5 7107 6 7119 7 7125 1 7125 8 7125 20 7137 2 7137 6 7143 2 7143 6 7143 24 7143 30 7149 3 7155 2 7155 5 7155 8 7155 13 7161 1 7161 15 7161 57 7167 8 7179 9 7179 11 7179 15 7179 39 7179 45 7185 8 7191 3 7191 9 7197 4 7203 10 7203 28 7203 32 7215 34 7221 185 7245 5 7245 12 7245 14 7245 17 7245 69 7245 102 7245 107 7257 10 7257 88 7263 8 7269 3 7275 1 7281 1 7281 17 7281 19 7293 4 7299 3 7305 3 7305 119 7305 128 7311 11 7317 12 7329 5 7329 61 7335 7 7335 11 7335 35 7341 15 7341 135 7347 2 7347 6 7347 8 7347 108 7353 8 7359 9 7365 4 7377 94 7383 10 7383 172 7389 11 7395 20 7401 3 7401 25 7419 7 7425 4 7443 4 7449 17 7455 60 7455 74 7473 6 7479 29 7485 12 7485 40 7485 57 7491 5 7503 2 7503 4 7515 17 7515 33 7521 3 7533 8 7533 52 7539 35 7539 75 7545 19 7545 31 7545 103 7551 37 7569 1 7569 159 7575 11 7575 25 7581 3 7593 16 7611 3 7617 2 7623 2 7623 30 7635 1 7635 6 7647 6 7653 6 7665 1 7665 10 7665 40 7671 5 7671 7 7671 35 7677 6 7695 3 7695 9 7695 93 7713 2 7719 33 7725 111 7731 5 7737 96 7737 166 7749 7 7749 9 7755 10 7755 17 7755 47 7767 26 7791 1 7797 10 7809 21 7809 29 7809 47 7821 1 7821 7 7845 6 7845 30 7851 5 7851 99 7857 8 7863 6 7863 22 7863 60 7869 1 7875 11 7881 103 7887 114 7917 6 7923 14 7929 61 7935 32 7947 222 7953 4 7977 12 7989 21 7995 5 7995 8 7995 47 8001 5 8001 15 8007 2 8007 4 8013 10 8019 3 8025 5 8031 1 8037 16 8037 76 8055 43 8061 77 8067 14 8067 26 8079 53 8085 44 8085 61 8091 25 8097 6 8097 46 8097 52 8103 2 8103 12 8109 11 8109 21 8115 1 8115 3 8115 10 8115 189 8121 53 8121 139 8127 18 8127 26 8133 2 8133 14 8133 34 8145 45 8157 24 8163 74 8175 8 8175 13 8181 1 8181 3 8193 6 8199 7 8205 7 8205 16 8205 26 8211 7 8211 35 8223 18 8223 28 8235 2 8235 5 8235 12 8235 27 8241 3 8241 21 8241 31 8253 4 8265 97 8265 199 8283 4 8289 5 8289 7 8289 13 8289 55 8295 2 8295 3 8319 21 8325 1 8325 10 8325 12 8325 70 8337 2 8337 192 8355 30 8367 6 8373 8 8373 10 8385 28 8397 2 8397 14 8409 3 8415 1 8415 11 8415 13 8415 23 8415 29 8415 38 8421 13 8421 15 8421 107 8427 52 8433 6 8445 5 8445 23 8451 1 8457 2 8457 56 8469 17 8475 4 8493 6 8499 5 8499 11 8499 25 8505 7 8505 51 8511 5 8511 49 8511 185 8517 6 8523 12 8535 3 8535 6 8535 39 8541 5 8541 47 8547 4 8547 8 8553 2 8559 43 8565 2 8565 15 8565 135 8571 45 8583 34 8589 3 8589 7 8595 1 8613 6 8619 37 8625 2 8625 44 8631 7 8631 9 8631 19 8649 3 8649 21 8655 6 8673 14 8673 18 8673 62 8679 83 8685 22 8691 11 8691 27 8697 6 8709 1 8709 5 8715 5 8715 6 8715 30 8721 127 8727 12 8727 60 8739 125 8745 1 8745 9 8745 12 8757 74 8763 2 8775 3 8775 51 8781 11 8787 16 8793 32 8799 1 8805 23 8811 3 8823 26 8829 1 8835 10 8841 1 8841 5 8841 9 8841 19 8841 29 8841 99 8847 14 8853 16 8859 5 8859 69 8865 3 8865 8 8877 2 8877 116 8883 2 8883 68 8895 1 8901 5 8907 6 8913 4 8919 1 8919 7 8919 31 8925 6 8949 5 8955 1 8955 21 8955 24 8961 1 8961 5 8973 4 8973 10 8979 1 8985 3 9003 2 9009 17 9021 1 9021 3 9021 9 9021 37 9027 2 9033 20 9033 50 9039 199 9051 13 9051 217 9057 20 9063 4 9063 6 9063 166 9069 23 9081 3 9087 16 9087 22 9087 34 9087 62 9093 16 9099 5 9105 4 9105 6 9105 13 9105 19 9105 60 9117 2 9117 8 9117 20 9123 4 9135 18 9135 24 9135 30 9141 25 9141 67 9159 15 9159 21 9165 13 9165 16 9189 51 9195 2 9195 12 9201 3 9207 82 9219 13 9225 2 9225 5 9225 11 9225 17 9225 101 9225 214 9231 3 9231 43 9237 24 9243 8 9249 15 9249 51 9255 2 9255 56 9261 1 9273 96 9279 9 9285 9 9285 77 9285 78 9291 15 9297 10 9297 20 9303 24 9327 2 9327 6 9345 3 9345 4 9345 55 9345 93 9357 4 9375 16 9381 5 9387 2 9387 20 9393 2 9405 27 9405 95 9411 17 9417 6 9423 2 9423 4 9435 4 9435 10 9435 76 9441 15 9453 2 9459 1 9459 37 9465 8 9465 35 9483 12 9483 34 9483 36 9489 5 9489 39 9495 78 9519 65 9525 6 9549 17 9555 5 9555 30 9555 91 9567 4 9585 6 9585 21 9591 1 9591 23 9591 47 9603 8 9609 3 9609 13 9615 2 9615 14 9615 17 9621 5 9621 17 9645 5 9651 67 9663 2 9681 11 9687 2 9687 10 9693 28 9693 42 9699 15 9699 99 9705 36 9711 1 9711 3 9717 10 9717 16 9723 22 9735 1 9741 5 9741 29 9747 48 9753 36 9753 196 9759 23 9765 21 9771 1 9789 9 9801 7 9801 35 9807 2 9807 24 9825 5 9825 6 9837 6 9843 2 9843 20 9849 1 9849 11 9849 121 9861 3 9861 33 9867 108 9873 32 9885 7 9885 32 9897 14 9903 6 9909 5 9909 65 9915 11 9915 245 9921 1 9945 1 9945 3 9945 16 9951 75 9957 2 9975 8 9975 11 9975 17 9975 61 9981 1 9987 4 9987 6 9987 18 9999 81 10005 4 10011 1 10011 61 10017 40 10017 112 10017 184 10023 32 10029 3 10035 9 10041 5 10047 4 10047 40 10059 3 10059 7 10059 9 10059 39 10065 199 10083 24 10083 104 10101 15 10107 2 10107 38 10125 92 10131 3 10131 13 10131 39 10137 70 10143 4
 2007-06-24, 07:38 #3 gd_barnes     May 2007 Kansas; USA 72·11·19 Posts Thanks, Citrix, for adding to my list. I think it's great to have a comprehensive list of all primes and twin primes of certain forms up to certain limits of k and n before going after the really big primes. For my list, I unofficially tested k=1 to 600 (i.e. ran no programs) up to the lower limit of where primes were tested to on the Riesel and Proth search sites by matching up the k's and n's. This has usually been up to at least n=200K because both Riesel and Proth primes have been mostly tested at least that high for all k's < 600. So I think doing any further twin testing for k < 600 would not be worthwile because even trying to find one twin above n=200K would take months and possibly years without a large coordinated effort. I have 3 decent-speed machines working on other prime efforts right now that I want to continue on for several weeks yet and a very slow older machine that I use for sieving while the others are prime testing. I think I'll do 3 things here to continue this process: 1. Specify exactly how far each of the k's on my list have been tested. Yours are specifically tested to n=250, but I can't say for sure how high of an n each k is tested on mine without looking more closely at the various sites. 2. Add your primes to my list. 3. Once my slow-speed machine (333 mhz) is done with it's current sieve in about 2 days, I'll use it to test your k's to higher n's for twins. As slow as it is, I'll either limit the n's to 1000 or limit the k's to 2000 and allow the n's to go up to 10000 or so. Obviously these are very rough estimates only. Also to be determined for my list...what gaps exist in the primes for the k's listed on the RPS, i.e. 15k, site, the Primesearch site, and the Proth search site. It's not immediately obvious where gaps exists. One gap that I know of for sure on Riesel primes is for k=289 from n=300K to n=501991. I checked around on another area in this forum and no one could say for sure that the range had been tested so I reserved it. I currently have my highest-speed dual-core machine working on the entire range. Any other Riesel prime that I find in that range will also be tested for a twin or checked for the same n on the Proth search site. Gary
2007-06-26, 08:19   #4
gd_barnes

May 2007
Kansas; USA

1024110 Posts
Combined list with testing limit included

Citrix,

Actually, k=1 to 600 have been searched enough since that's how far the Proth search site goes up to and so is how far up I matched the site with ours.

I wasn't able to do any more testing yet but I combined your list with mine and added the value of n that each k has been tested through. Of course all of yours are 250. I also added odd k's divisbile by 3 (i.e. k=3 mod 6) up to k < 1000 where no twins were found and showed (none) by them. People might like to test those with a little more vigor in the future. I suspect there will be plenty of k's that have no twin primes found. It will be interesting to see if the lowest value of k=3 mod 6 where there are no twins really turns out to be k=111 like it is now. It has technically been tested to n=350K.

I should be able to extend the search for k > 600 a little on Tuesday sometime. Thanks for your help so far. This might turn out to be an interesting effort and could give us a good base to work from if we wish to find somewhat large triplets, quadruplets, 5-tuples, etc. in the future.

My changes are attached.

Gary
Attached Files
 twin primes match.txt (24.7 KB, 401 views)

Last fiddled with by gd_barnes on 2007-06-26 at 08:22

 2007-06-28, 04:19 #5 Citrix     Jun 2003 32×52×7 Posts Twins upto n=500. These twins are really rare.. 165 264 165 282 555 282 573 344 615 391 669 333 969 269 1023 380 1215 255 1701 387 1743 418 1899 291 1995 492 2085 455 2373 294 2475 260 2565 468 2667 288 2805 259 3321 371 3381 281 3921 443 4101 443 4323 458 5049 361 5139 251 5253 338 5415 435 5547 470 6405 299 7173 294 7503 488 7605 314 7785 355 7791 331 8613 458 8787 472 9063 456 9129 359 9345 445 9369 365 9543 310 9609 297 9789 263 9951 257 9993 308 10071 327
2007-06-28, 04:35   #6
gd_barnes

May 2007
Kansas; USA

72·11·19 Posts
Complete twin list k=1-100K and n=1-5K

Attached is a complete list of all twin primes for k = 1 to 100K and n = 1 to 5K for the form k * 2^n +/- 1. It also includes the twin 459 * 2 ^ 8529 +/- 1 from my earlier effort to match up all known Riesel and Proth primes. There are a total of 17717 twins in the list.

I hope someone finds this useful in searches for more 'exotic' primes such as triplets, quads, 5-tuples, etc.

Eventually I want to expand the list for all k < 1M and all n < 100K. If anyone wants to contribute to the effort, let me know. I'll be sieving to n=10K later this week, which won't take long.

n's > 66K make the current top-20 twin prime list.

Gary
Attached Files
 twin primes k=1-100K n=1-5K.txt (224.3 KB, 568 views)

Last fiddled with by gd_barnes on 2007-06-28 at 05:05

2007-06-28, 05:02   #7
gd_barnes

May 2007
Kansas; USA

72·11·19 Posts
How sieving multiple k's and n's on twins ?

Quote:
 Originally Posted by Citrix Twins upto n=500. These twins are really rare..
Sorry we duplicated efforts there Citrix. Yes, twins are rare, which makes them special. Imagine triplets or quads! I checked my new extended list and all of yours are on there.

I'm curious...how are you sieving multiple k's and n's on twins? Here's what I'm doing but I'm thinking there must be a better way:

1. Use NewPGen and have it increment the n by 1 each time after it searches the range of k (in my case was 1 to 100000) that I want. For n < 2500, I just let it do each n almost instantly by sieving to only 1M since LLR is finding them rapidly. For n > 2500, I sieved to 100M. But these were just guesses because of the problem in #2.

2. #1 has the annoying problem of creating 1 file for each n, which I can't seem to get around. So I'm forced to then copy all of the files into one big file. I've been doing them 500 n's at a time.

3. Fortunately LLR, being the great program that it is, is able to accept one big file with many lines of XXXX:T:0:2:3 throughout the middle of it so it's able to handle many k's and n's in the same file.

I found the above to still be far faster than attempting to use the very slow Proth program and letting it both sieve and find primes. Do you know of a faster (or at least cleaner) way to sieve multiple k's and n's into one file? If there's some other software out there that would be better, could you provide a link to it? I get all of these various sites confused at times.

It doesn't take too long to copy 500 files into 1 file and then delete the 500 files. But the main problem with it only sieving 1 n at a time is that I can't get an accurate estimate of how many primes are being removed per second. I mean for 1 n, it might be removing only 1 per second but if it were sieving all 500 n at once, it might be removing 500 per second. But I don't know yet because in only sieving to 100M, it finishes fast enough that it doesn't show the rate. I finally resorted to just writing down the starting and ending time on my watch to determine how much total sieving and LLR time it was taking for each range of 500 n to get an idea of when to increase my sieve limit.

Thanks,
Gary

 2007-06-28, 20:37 #8 Joshua2     Sep 2004 21516 Posts What is the goal of all this? Is it supposed to help the TPS project some way? I don't quite get what you guys are doing.
2007-06-29, 06:56   #9
gd_barnes

May 2007
Kansas; USA

72·11·19 Posts
It's in the process

Quote:
 Originally Posted by Joshua2 What is the goal of all this? Is it supposed to help the TPS project some way? I don't quite get what you guys are doing.
What is our goal? We're finding twin primes! I believe the goal of these forums is to find all of the primes of certain forms; not just the large ones. Our goal here is to find all of the TWIN primes of a certain form. Some people prefer to find very few large primes. We here prefer to find all of the small primes and gradually build our way up to the large primes. Since very few people are interested in this sort of 'dirty work', that is our task here. This is no different than our < 300 site. It doesn't show just large primes, it shows them all.

The great 19th-century mathematician Carl Friedrich Gauss didn't start trying to manually calculate prime numbers beginning at 1 billion or higher just to make a big splash or set some sort of calculation record. He painstakingly started where others had left off and manually calculated ALL primes up to 3 million in order to construct some of the greatest mathematical proofs and theories of all time.

It is only in the painstaking process of starting with the elementary building blocks of a process that one can glean the information needed in order to gain a deeper understanding of the process as a whole.

Gary

Last fiddled with by gd_barnes on 2007-06-29 at 07:27 Reason: spelling/grammar

2007-07-03, 20:39   #10
gd_barnes

May 2007
Kansas; USA

240018 Posts
List of twins completed to n=10K

I've completed searching for twins up to n=10K for k=1 to 100K. The list is attached. There are only 23 twins between n=5K and 10K. I can see that I'm going to need to expand the list up to k=1M or 10M to get any significant # of twins for n>10K. (no surprise there!)

I also checked the list for triplets and quadruplets. The largest of all 3 kinds that I've found so far are:

Twins: 33891*2^9869-1,+1

Triplets: 32811*2^2707-1,+1,+5

I also checked triplets and quads for the form of k*2^n-7,-5,-1,+1 and k*2^n-5,-1,+1 but there were none as large.

-7, -5, +5, and +7 primes were checked at http://www.alpertron.com.ar/ECM.HTM. The largest ones were also checked with Primo software.

Although the list looks small now, it only takes an exponent of 10475 to make the top-10 triplets list and an exponent of 3489 to make the top-10 quads list. Largest k-tuplets are shown at www.ltkz.demon.co.uk/ktuplets.htm.

Gary
Attached Files
 twin primes k=1-100K n=1-10K.txt (214.7 KB, 420 views)

2007-08-21, 02:40   #11
gd_barnes

May 2007
Kansas; USA

240018 Posts
TPS extended to n=15K up to k < 1M.

I have now extended the Riesel-Proth twin prime search up to n=15K for all k < 1M.

I am attaching two lists:
1. The original list for k < 100K extended to n=15K sorted by k. 8 additional twins were found at this low level of k. To find them easily, you'll probably need to look at the list in #2.

2. A new list for k < 1M for 10K < n <= 15K sorted by n. There were a total of 85 twins in this range. Note that it includes the 8 twins from #1.

The most interesting find was 915 * 2 ^ 11455 +/- 1. It is the only twin that I've seen where k is < 1K and n is > 10K. In doing a search of the top-5000 site archives for twins, I see that it has already been found but there are none greater for k < 1K. A further analysis of the top-5000 archives shows that 80 of these 85 twins were never stored there so there is plenty of new information here.

I did tests for both +5 and -5 triplets on all 85 new twins. None were found. Eventually it would be interesting to extend the k to 1M for n < 10K and see if some higher triplets or quads can be found then what was posted last time but NOT to list more small twins. The chances are slim that a triplet or quad will be found for k < 1M for n > 15K.

I am now sieving for twins in the range of 15K < n <= 20K and k < 1M.

Gary
Attached Files
 twin primes n=1-15K.zip (61.7 KB, 252 views)

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