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Old 2021-04-13, 07:25   #1079
garambois
 
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"Garambois Jean-Luc"
Oct 2011
France

2·7·41 Posts
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Quote:
Originally Posted by Happy5214 View Post
I dared, and I came up short. It took two hours with 8 threads on my Kubuntu Focus, and it generated over 39 MB of factors. More than half of the time was spent on the sigma calculation Thanks to changes to my code (available on GitHub) that also output the abundance ratio (I also added changes to the argument passing and the ability to pass the exponent via a file), I was able to grep the output (which had been redirected to a file) and see this:

Code:
Index 1 of 3^5722[...]9375 is not abundant. (0.96466)
Sorry. It only improved from 0.936224 at 30000000, so I think you'll have to go for k.
OK, I have an exponent k :
Code:
k = 
3^8 * 5^7 * 7^5 * 11^4 * 13^4 * 17^3 * 19^3 * 23^2 * 29^3 * 31^2 * 37^3 *  41^2 * 43^2 * 47^2 * 53^2 * 59^2 * 61^2 * 67^2 * 71^2 * 73^2 * 79^2 *  83^2 * 89^2 * 97^2 * 101 * 103 * 107 * 109^2 * 113^2 * 127^2 * 131^2 *  137 * 139 * 149 * 151^2 * 157 * 163 * 167 * 173 * 179 * 181 * 191^2 *  193 * 197 * 199 * 211^2 * 223 * 227 * 229 * 233^2 * 239^2 * 241 * 251 *  257 * 263 * 269 * 271^2 * 277 * 281 * 283^2 * 293 * 307 * 311 * 313 *  317 * 331 * 337 * 347 * 349 * 353 * 359 * 367 * 373 * 379 * 383 * 389 *  397 * 401 * 409 * 419 * 421 * 431 * 433 * 439 * 443 * 449 * 457 * 461 *  463 * 467 * 479 * 487 * 491 * 499 * 503 * 509 * 521 * 523 * 541 * 547 *  557 * 563 * 569 * 571 * 577 * 587 * 593 * 599 * 601 * 607 * 613 * 617 *  619 * 631 * 641 * 643 * 647 * 653 * 659 * 661 * 673 * 677 * 683 * 691 *  701 * 709 * 719 * 727 * 733 * 739 * 743 * 751 * 757 * 761 * 769 * 773 *  787 * 797 * 809 * 811 * 821 * 823 * 827 * 829 * 839 * 853 * 857 * 859 *  863 * 877 * 881 * 883 * 887 * 907 * 911 * 919 * 929 * 937 * 941 * 947 *  953 * 967 * 971 * 977 * 983 * 991 * 997 * 1009 * 1013 * 1019 * 1021 *  1031 * 1033 * 1039 * 1049 * 1051 * 1061 * 1063 * 1069 * 1087 * 1091 *  1093 * 1097 * 1103 * 1109 * 1117 * 1123 * 1129 * 1151 * 1153 * 1163 *  1171 * 1181 * 1187 * 1193 * 1201 * 1213 * 1217 * 1223 * 1229 * 1231 *  1237 * 1249 * 1259 * 1277 * 1279 * 1283 * 1289 * 1291 * 1297 * 1301 *  1303 * 1307 * 1319 * 1321 * 1327 * 1361 * 1367 * 1373 * 1381 * 1399 *  1409 * 1423 * 1427 * 1429 * 1433 * 1439 * 1447 * 1451 * 1453 * 1459 *  1471 * 1481 * 1483 * 1487 * 1489 * 1493 * 1499 * 1511 * 1523 * 1531 *  1543 * 1549 * 1553 * 1559 * 1567 * 1571 * 1579 * 1583 * 1597 * 1601 *  1607 * 1609 * 1613 * 1619 * 1621 * 1627 * 1637 * 1657 * 1663 * 1667 *  1669 * 1693 * 1697 * 1699 * 1709 * 1721 * 1723 * 1733 * 1741 * 1747 *  1753 * 1759 * 1777 * 1783 * 1787 * 1789 * 1801 * 1811 * 1823 * 1831 *  1847 * 1861 * 1867 * 1871 * 1873 * 1877 * 1879 * 1889 * 1901 * 1907 *  1913 * 1931 * 1933 * 1949 * 1951 * 1973 * 1979 * 1987 * 1993 * 1997 *  1999 * 2003 * 2011 * 2017 * 2027 * 2029 * 2039 * 2053 * 2063 * 2069 *  2081 * 2083 * 2087 * 2089 * 2099 * 2111 * 2113 * 2129 * 2131 * 2137 *  2141 * 2143 * 2153 * 2161 * 2179 * 2203 * 2207 * 2213 * 2221 * 2237 *  2239 * 2243 * 2251 * 2267 * 2269 * 2273 * 2281 * 2287 * 2293 * 2297 *  2309 * 2311 * 2333 * 2339 * 2341 * 2347 * 2351 * 2357 * 2371 * 2377 *  2381 * 2383 * 2389 * 2393 * 2399 * 2411 * 2417 * 2423 * 2437 * 2441 *  2447 * 2459 * 2467 * 2473 * 2477 * 2503 * 2521 * 2531 * 2539 * 2543 *  2549 * 2551 * 2557 * 2579 * 2591 * 2593 * 2609 * 2617 * 2621 * 2633 *  2647 * 2657 * 2659 * 2663 * 2671 * 2677 * 2683 * 2687 * 2689 * 2693 *  2699 * 2707 * 2711 * 2713 * 2719 * 2729 * 2731 * 2741 * 2749 * 2753 *  2767 * 2777 * 2789 * 2791 * 2797 * 2801 * 2803 * 2819 * 2833 * 2837 *  2843 * 2851 * 2857 * 2861 * 2887 * 2897 * 2903 * 2909 * 2917 * 2927 *  2939 * 2953 * 2957 * 2963 * 2969 * 2971 * 2999 * 3001 * 3011 * 3019 *  3023 * 3037 * 3041 * 3049 * 3061 * 3067 * 3079 * 3083 * 3089 * 3109 *  3119 * 3121 * 3137 * 3163 * 3167 * 3169 * 3187 * 3191 * 3203 * 3209 *  3217 * 3221 * 3229 * 3251 * 3253 * 3257 * 3259 * 3271 * 3299 * 3301 *  3307 * 3313 * 3319 * 3323 * 3329 * 3331 * 3343 * 3347 * 3359 * 3361 *  3371 * 3373 * 3389 * 3391 * 3407 * 3413 * 3433 * 3449 * 3457 * 3461 *  3463 * 3467 * 3469 * 3491 * 3499 * 3511 * 3517 * 3527 * 3529 * 3533 *  3539 * 3541 * 3547 * 3557 * 3559 * 3571 * 3581 * 3583 * 3593 * 3607 *  3613 * 3617 * 3623 * 3631 * 3643 * 3659 * 3671 * 3673 * 3677 * 3691 *  3697 * 3701 * 3709 * 3719 * 3727 * 3733 * 3739 * 3761 * 3767 * 3769 *  3779 * 3793 * 3797 * 3803 * 3821 * 3823 * 3833 * 3847 * 3851 * 3853 *  3863 * 3877 * 3881 * 3889 * 3911 * 3919 * 3923 * 3929 * 3931 * 3943 *  3947 * 3967 * 3989 * 4001 * 4003 * 4007 * 4013 * 4019 * 4021 * 4027 *  4049 * 4051 * 4057 * 4073 * 4079 * 4091 * 4093 * 4099 * 4111 * 4127 *  4129 * 4133 * 4139 * 4153 * 4157 * 4159 * 4177 * 4201 * 4211 * 4217 *  4219 * 4229 * 4231 * 4241 * 4253 * 4259 * 4261 * 4271 * 4273 * 4283 *  4289 * 4297 * 4327 * 4337 * 4339 * 4349 * 4357 * 4363 * 4373 * 4391 *  4397 * 4409 * 4423 * 4441 * 4447 * 4451 * 4457 * 4463 * 4481 * 4483 *  4493 * 4513 * 4517 * 4519 * 4523 * 4547 * 4549 * 4561 * 4583 * 4591 *  4597 * 4603 * 4621 * 4637 * 4639 * 4643 * 4649 * 4651 * 4657 * 4663 *  4673 * 4679 * 4691 * 4703 * 4721 * 4723 * 4729 * 4733 * 4751 * 4759 *  4783 * 4787 * 4789 * 4793 * 4799 * 4801 * 4813 * 4817 * 4831 * 4861 *  4871 * 4877 * 4889 * 4903 * 4909 * 4919 * 4931 * 4933 * 4937 * 4943 *  4951 * 4967 * 4973 * 4987 * 4993 * 4999 * 5003 * 5011 * 5021 * 5023 *  5039 * 5051 * 5059 * 5077 * 5081 * 5087 * 5099 * 5101 * 5107 * 5113 *  5119 * 5147 * 5153 * 5167 * 5171 * 5179 * 5189 * 5197 * 5209 * 5231 *  5233 * 5237 * 5261 * 5273 * 5279 * 5281 * 5297 * 5303 * 5323 * 5333 *  5351 * 5381 * 5387 * 5393 * 5399 * 5407 * 5413 * 5419 * 5431 * 5437 *  5441 * 5443 * 5449 * 5471 * 5477 * 5479 * 5483 * 5501 * 5503 * 5507 *  5519 * 5521 * 5527 * 5531 * 5557 * 5563 * 5569 * 5573 * 5581 * 5623 *  5639 * 5647 * 5651 * 5653 * 5657 * 5659 * 5669 * 5683 * 5689 * 5701 *  5711 * 5717 * 5737 * 5741 * 5749 * 5779 * 5783 * 5791 * 5801 * 5807 *  5813 * 5821 * 5827 * 5839 * 5849 * 5851 * 5857 * 5867 * 5869 * 5879 *  5897 * 5903 * 5923 * 5927 * 5939 * 5953 * 5981 * 5987 * 6007 * 6011 *  6029 * 6037 * 6043 * 6047 * 6053 * 6067 * 6079 * 6089 * 6091 * 6101 *  6113 * 6121 * 6131 * 6133 * 6151 * 6163 * 6173 * 6197 * 6199 * 6203 *  6211 * 6217 * 6221 * 6229 * 6257 * 6263 * 6269 * 6271 * 6287 * 6299 *  6311 * 6317 * 6323 * 6329 * 6337 * 6343 * 6353 * 6361 * 6367 * 6373 *  6379 * 6397 * 6421 * 6427 * 6449 * 6469 * 6473 * 6481 * 6491 * 6521 *  6551 * 6553 * 6563 * 6569 * 6571 * 6581 * 6599 * 6607 * 6619 * 6637 *  6653 * 6659 * 6661 * 6673 * 6679 * 6689 * 6691 * 6709 * 6719 * 6733 *  6737 * 6761 * 6763 * 6779 * 6781 * 6793 * 6803 * 6823 * 6829 * 6833 *  6841 * 6863 * 6869 * 6871 * 6883 * 6899 * 6911 * 6947 * 6949 * 6959 *  6961 * 6967 * 6971 * 6977 * 6983 * 6991 * 6997 * 7001 * 7013 * 7019 *  7027 * 7039 * 7043 * 7057 * 7079 * 7103 * 7109 * 7121 * 7127 * 7129 *  7151 * 7159 * 7177 * 7187 * 7193 * 7207 * 7211 * 7213 * 7219 * 7229 *  7243 * 7247 * 7253 * 7283 * 7297 * 7307 * 7309 * 7321 * 7331 * 7333 *  7349 * 7351 * 7369 * 7393 * 7411 * 7433 * 7451 * 7457 * 7477 * 7481 *  7487 * 7489 * 7499 * 7507 * 7517 * 7523 * 7529 * 7537 * 7541 * 7547 *  7559 * 7561 * 7573 * 7577 * 7583 * 7591 * 7603 * 7607 * 7621 * 7639 *  7643 * 7649 * 7669 * 7673 * 7681 * 7687 * 7691 * 7699 * 7703 * 7717 *  7723 * 7727 * 7741 * 7753 * 7759 * 7793 * 7817 * 7823 * 7829 * 7841 *  7853 * 7867 * 7873 * 7877 * 7879 * 7883 * 7901 * 7927 * 7933 * 7937 *  7963 * 7993 * 8009 * 8011 * 8053 * 8069 * 8081 * 8087 * 8089 * 8093 *  8101 * 8111 * 8117 * 8123 * 8147 * 8161 * 8167 * 8171 * 8179 * 8191 *  8219 * 8231 * 8237 * 8243 * 8263 * 8269 * 8273 * 8287 * 8291 * 8297 *  8317 * 8329 * 8353 * 8363 * 8369 * 8377 * 8387 * 8389 * 8419 * 8431 *  8443 * 8447 * 8461 * 8467 * 8501 * 8513 * 8521 * 8543 * 8573 * 8597 *  8599 * 8609 * 8623 * 8627 * 8629 * 8641 * 8663 * 8669 * 8677 * 8681 *  8693 * 8699 * 8707 * 8713 * 8719 * 8731 * 8741 * 8761 * 8779 * 8783 *  8807 * 8819 * 8821 * 8837 * 8849 * 8863 * 8867 * 8923 * 8929 * 8933 *  8951 * 8969 * 9001 * 9007 * 9011 * 9013 * 9029 * 9041 * 9043 * 9049 *  9059 * 9091 * 9103 * 9109 * 9133 * 9151 * 9157 * 9161 * 9173 * 9181 *  9203 * 9209 * 9221 * 9239 * 9241 * 9281 * 9283 * 9293 * 9311 * 9319 *  9323 * 9337 * 9343 * 9349 * 9371 * 9391 * 9397 * 9403 * 9413 * 9419 *  9431 * 9433 * 9439 * 9473 * 9479 * 9511 * 9521 * 9539 * 9547 * 9551 *  9587 * 9601 * 9619 * 9629 * 9643 * 9677 * 9689 * 9719 * 9733 * 9743 *  9749 * 9767 * 9781 * 9787 * 9791 * 9803 * 9817 * 9839 * 9851 * 9857 *  9871 * 9883 * 9887 * 9923 * 9929 * 9941 * 9949 * 9967 * 9973 * 10007 *  10009 * 10039 * 10061 * 10067 * 10069 * 10079 * 10091 * 10093 * 10099 *  10103 * 10111 * 10133 * 10141 * 10151 * 10159 * 10163 * 10169 * 10177 *  10211 * 10223 * 10243 * 10253 * 10271 * 10301 * 10303 * 10313 * 10331 *  10333 * 10337 * 10357 * 10391 * 10399 * 10433 * 10459 * 10463 * 10477 *  10487 * 10499 * 10513 * 10529 * 10559 * 10589 * 10597 * 10601 * 10607 *  10613 * 10627 * 10639 * 10651 * 10663 * 10667 * 10687 * 10691 * 10709 *  10723 * 10729 * 10733 * 10753 * 10781 * 10789 * 10799 * 10837 * 10847 *  10859 * 10867 * 10883 * 10889 * 10891 * 10937 * 10939 * 10949 * 10957 *  10973 * 10987 * 11003 * 11057 * 11059 * 11071 * 11083 * 11087 * 11093 *  11113 * 11117 * 11119 * 11131 * 11149 * 11159 * 11161 * 11171 * 11173 *  11197 * 11257 * 11261 * 11273 * 11279 * 11311 * 11317 * 11321 * 11329 *  11353 * 11369 * 11393 * 11399 * 11423 * 11437 * 11443 * 11467 * 11471 *  11489 * 11519 * 11549 * 11579 * 11587 * 11593 * 11597 * 11621 * 11633 *  11657 * 11677 * 11681 * 11689 * 11699 * 11717 * 11719 * 11731 * 11743 *  11779 * 11783 * 11789 * 11801 * 11813 * 11821 * 11831 * 11833 * 11863 *  11903 * 11909 * 11927 * 11933 * 11939 * 11953 * 11959 * 11981 * 11987 *  12011 * 12037 * 12041 * 12043 * 12073 * 12101 * 12109 * 12113 * 12119 *  12143 * 12149 * 12157 * 12161 * 12163 * 12197 * 12203 * 12211 * 12227 *  12263 * 12289 * 12301 * 12323 * 12329 * 12347 * 12373 * 12379 * 12391 *  12409 * 12413 * 12421 * 12433 * 12451 * 12491 * 12497 * 12511 * 12527 *  12539 * 12547 * 12583 * 12601 * 12613 * 12637 * 12641 * 12653 * 12671 *  12689 * 12697 * 12703 * 12739 * 12743 * 12757 * 12781 * 12791 * 12809 *  12821 * 12823 * 12829 * 12841 * 12853 * 12889 * 12893 * 12899 * 12911 *  12919 * 12923 * 12959 * 12967 * 12983 * 13001 * 13003 * 13007 * 13009 *  13033 * 13037 * 13043 * 13049 * 13063 * 13099 * 13103 * 13109 * 13121 *  13147 * 13151 * 13159 * 13171 * 13177 * 13187 * 13217 * 13229 * 13249 *  13291 * 13297 * 13313 * 13327 * 13339 * 13367 * 13381 * 13397 * 13399 *  13417 * 13421 * 13441 * 13451 * 13463 * 13469 * 13513 * 13537 * 13553 *  13567 * 13577 * 13591 * 13597 * 13613 * 13619 * 13649 * 13669 * 13679 *  13681 * 13693 * 13721 * 13723 * 13729 * 13763 * 13789 * 13799 * 13807 *  13829 * 13831 * 13859 * 13873 * 13877 * 13879 * 13883 * 13901 * 13903 *  13913 * 13967 * 13999 * 14009 * 14011 * 14057 * 14081 * 14083 * 14143 *  14153 * 14159 * 14173 * 14177 * 14197 * 14207 * 14221 * 14243 * 14249 *  14281 * 14303 * 14321 * 14323 * 14341 * 14407 * 14423 * 14431 * 14437 *  14461 * 14479 * 14489 * 14503 * 14519 * 14533 * 14551 * 14557 * 14561 *  14593 * 14621 * 14627 * 14629 * 14669 * 14683 * 14699 * 14731 * 14741 *  14767 * 14779 * 14783 * 14813 * 14831 * 14843 * 14851 * 14869 * 14879 *  14891 * 14923 * 14929 * 14939 * 14983 * 15013 * 15061 * 15083 * 15101 *  15139 * 15149 * 15161 * 15173 * 15187 * 15233 * 15241 * 15259 * 15269 *  15277 * 15287 * 15289 * 15307 * 15319 * 15329 * 15349 * 15359 * 15361 *  15373 * 15383 * 15391 * 15401 * 15427 * 15461 * 15473 * 15527 * 15569 *  15601 * 15607 * 15629 * 15643 * 15649 * 15667 * 15679 * 15683 * 15727 *  15731 * 15733 * 15739 * 15773 * 15791 * 15803 * 15823 * 15859 * 15877 *  15881 * 15889 * 15907 * 15919 * 15923 * 15959 * 15971 * 15991 * 16001 *  16033 * 16073 * 16091 * 16097 * 16139 * 16141 * 16183 * 16189 * 16249 *  16253 * 16267 * 16273 * 16301 * 16333 * 16361 * 16369 * 16381 * 16421 *  16427 * 16447 * 16451 * 16453 * 16477 * 16493 * 16553 * 16561 * 16603 *  16619 * 16649 * 16651 * 16657 * 16673 * 16691 * 16693 * 16699 * 16703 *  16729 * 16741 * 16747 * 16811 * 16823 * 16831 * 16843 * 16883 * 16931 *  16943 * 16981 * 17011 * 17021 * 17033 * 17077 * 17123 * 17137 * 17159 *  17167 * 17183 * 17203 * 17291 * 17299 * 17317 * 17321 * 17333 * 17351 *  17359 * 17389 * 17401 * 17417 * 17419 * 17431 * 17443 * 17449 * 17483 *  17497 * 17509 * 17519 * 17539 * 17551 * 17569 * 17573 * 17579 * 17581 *  17599 * 17627 * 17659 * 17669 * 17681 * 17713 * 17891 * 17903 * 17909 *  17911 * 17939 * 17959 * 17977 * 17981 * 18013 * 18041 * 18043 * 18049 *  18119 * 18121 * 18127 * 18131 * 18143 * 18149 * 18191 * 18199 * 18211 *  18223 * 18229 * 18233 * 18269 * 18289 * 18313 * 18329 * 18341 * 18367 *  18397 * 18401 * 18413 * 18427 * 18433 * 18443 * 18451 * 18457 * 18461 *  18503 * 18517 * 18523 * 18553 * 18583 * 18587 * 18617 * 18679 * 18731 *  18757 * 18773 * 18787 * 18793 * 18803 * 18869 * 18899 * 18917 * 18919 *  19001 * 19009 * 19069 * 19081 * 19087 * 19141 * 19157 * 19163 * 19183 *  19219 * 19259 * 19301 * 19319 * 19373 * 19379 * 19381 * 19387 * 19391 *  19421 * 19423 * 19427 * 19429 * 19433 * 19441 * 19447 * 19477 * 19489 *  19501 * 19507 * 19531 * 19553 * 19559 * 19583 * 19597 * 19661 * 19687 *  19699 * 19709 * 19751 * 19853 * 19889 * 19913 * 19919 * 19949 * 19991 *  19993 * 20023 * 20063 * 20071 * 20089 * 20101 * 20129 * 20143 * 20149 *  20201 * 20219 * 20249 * 20359 * 20369 * 20393 * 20399 * 20411 * 20441 *  20521 * 20551 * 20639 * 20641 * 20663 * 20681 * 20693 * 20719 * 20753 *  20759 * 20771 * 20773 * 20789 * 20807 * 20879 * 20887 * 20899 * 20921 *  20939 * 20947 * 20963 * 20981 * 20983 * 21001 * 21011 * 21013 * 21023 *  21059 * 21067 * 21089 * 21149 * 21179 * 21221 * 21283 * 21323 * 21341 *  21379 * 21383 * 21401 * 21419 * 21499 * 21521 * 21523 * 21529 * 21559 *  21577 * 21601 * 21611 * 21647 * 21661 * 21673 * 21701 * 21713 * 21737 *  21767 * 21799 * 21803 * 21871 * 21881 * 21893 * 21929 * 22003 * 22013 *  22027 * 22051 * 22067 * 22079 * 22091 * 22093 * 22111 * 22133 * 22153 *  22189 * 22259 * 22271 * 22277 * 22279 * 22303 * 22343 * 22349 * 22369 *  22391 * 22409 * 22433 * 22469 * 22481 * 22511 * 22541 * 22543 * 22613 *  22619 * 22621 * 22637 * 22643 * 22651 * 22751 * 22777 * 22817 * 22853 *  22921 * 22937 * 22943 * 22963 * 22993 * 23003 * 23011 * 23027 * 23029 *  23099 * 23143 * 23189 * 23203 * 23209 * 23279 * 23321 * 23339 * 23357 *  23459 * 23509 * 23531 * 23539 * 23549 * 23561 * 23581 * 23593 * 23603 *  23609 * 23663 * 23669 * 23671 * 23743 * 23753 * 23789 * 23801 * 23813 *  23819 * 23873 * 23909 * 23917 * 23957 * 23981 * 24001 * 24023 * 24029 *  24043 * 24049 * 24061 * 24071 * 24077 * 24083 * 24097 * 24107 * 24109 *  24121 * 24151 * 24203 * 24223 * 24239 * 24251 * 24281 * 24373 * 24379 *  24391 * 24439 * 24469 * 24473 * 24481 * 24499 * 24509 * 24533 * 24547 *  24551 * 24611 * 24659 * 24683 * 24697 * 24709 * 24733 * 24749 * 24763 *  24799 * 24821 * 24841 * 24851 * 24859 * 24877 * 24889 * 24917 * 24919 *  24967 * 24971 * 24979 * 25033 * 25057 * 25073 * 25087 * 25111 * 25171 *  25183 * 25219 * 25229 * 25301 * 25309 * 25411 * 25457 * 25469 * 25523 *  25537 * 25579 * 25601 * 25603 * 25639 * 25643 * 25673 * 25703 * 25759 *  25763 * 25799 * 25841 * 25913 * 25919 * 25931 * 25969 * 25997 * 25999 *  26029 * 26111 * 26119 * 26189 * 26251 * 26261 * 26293 * 26317 * 26393 *  26423 * 26459 * 26479 * 26489 * 26501 * 26513 * 26573 * 26591 * 26633 *  26641 * 26711 * 26759 * 26801 * 26813 * 26833 * 26849 * 26861 * 26879 *  26891 * 26893 * 26951 * 26953 * 26993 * 27031 * 27043 * 27091 * 27107 *  27143 * 27239 * 27241 * 27281 * 27361 * 27397 * 27449 * 27479 * 27481 *  27527 * 27539 * 27551 * 27581 * 27583 * 27743 * 27749 * 27773 * 27779 *  27793 * 27799 * 27809 * 27893 * 27943 * 27947 * 27983 * 28001 * 28019 *  28031 * 28051 * 28123 * 28163 * 28277 * 28349 * 28403 * 28411 * 28439 *  28463 * 28499 * 28537 * 28549 * 28559 * 28571 * 28573 * 28643 * 28723 *  28751 * 28753 * 28759 * 28793 * 28807 * 28837 * 28843 * 28859 * 28871 *  28901 * 28933 * 28949 * 28961 * 29017 * 29021 * 29033 * 29059 * 29063 *  29123 * 29137 * 29167 * 29201 * 29209 * 29269 * 29339 * 29363 * 29401 *  29429 * 29437 * 29443 * 29453 * 29483 * 29531 * 29573 * 29599 * 29629 *  29683 * 29723 * 29741 * 29759 * 29819 * 29851 * 29863 * 29867 * 29873 *  29881 * 29947 * 30029 * 30071 * 30113 * 30269 * 30313 * 30319 * 30323 *  30389 * 30431 * 30449 * 30577 * 30631 * 30649 * 30671 * 30689 * 30773 *  30803 * 30809 * 30817 * 30851 * 30937 * 30983 * 31019 * 31033 * 31069 *  31079 * 31121 * 31151 * 31153 * 31159 * 31193 * 31231 * 31249 * 31253 *  31271 * 31277 * 31319 * 31327 * 31469 * 31513 * 31541 * 31583 * 31649 *  31663 * 31699 * 31721 * 31727 * 31741 * 31771 * 31793 * 31799 * 31859 *  31963 * 31981 * 32003 * 32009 * 32027 * 32063 * 32141 * 32159 * 32309 *  32353 * 32381 * 32411 * 32479 * 32531 * 32561 * 32569 * 32573 * 32633 *  32647 * 32693 * 32719 * 32771 * 32789 * 32803 * 32843 * 32933 * 32941 *  33023 * 33029 * 33053 * 33113 * 33119 * 33179 * 33191 * 33203 * 33223 *  33349 * 33353 * 33413 * 33461 * 33479 * 33521 * 33569 * 33623 * 33713 *  33749 * 33773 * 33809 * 33829 * 33857 * 33941 * 34019 * 34213 * 34253 *  34283 * 34319 * 34421 * 34439 * 34487 * 34537 * 34591 * 34613 * 34631 *  34673 * 34849 * 34883 * 34913 * 34949 * 35069 * 35081 * 35089 * 35099 *  35111 * 35117 * 35281 * 35291 * 35353 * 35437 * 35533 * 35537 * 35573 *  35617 * 35831 * 35923 * 35933 * 35993 * 35999 * 36007 * 36083 * 36109 *  36151 * 36191 * 36229 * 36251 * 36299 * 36353 * 36383 * 36473 * 36479 *  36563 * 36629 * 36749 * 36761 * 36791 * 36821 * 36923 * 36929 * 36979 *  37013 * 37039 * 37049 * 37057 * 37087 * 37139 * 37181 * 37253 * 37277 *  37309 * 37313 * 37321 * 37337 * 37379 * 37409 * 37423 * 37537 * 37549 *  37619 * 37699 * 37783 * 37853 * 37871 * 37991 * 38011 * 38039 * 38113 *  38149 * 38183 * 38189 * 38201 * 38231 * 38303 * 38317 * 38333 * 38453 *  38459 * 38501 * 38629 * 38639 * 38669 * 38723 * 38861 * 38867 * 38873 *  38891 * 38923 * 38933 * 38953 * 39023 * 39089 * 39113 * 39119 * 39233 *  39239 * 39359 * 39373 * 39383 * 39409 * 39419 * 39443 * 39521 * 39551 *  39569 * 39659 * 39769 * 39779 * 39863 * 39901 * 39953 * 39971 * 39979 *  39983 * 39989 * 40129 * 40163 * 40193 * 40283 * 40343 * 40429 * 40543 *  40559 * 40709 * 40763 * 40787 * 40813 * 40823 * 40853 * 40949 * 41017 *  41081 * 41161 * 41189 * 41203 * 41221 * 41231 * 41243 * 41381 * 41387 *  41399 * 41413 * 41513 * 41593 * 41597 * 41603 * 41609 * 41621 * 41669 *  41719 * 41729 * 41809 * 41893 * 41969 * 42019 * 42023 * 42071 * 42089 *  42131 * 42221 * 42359 * 42409 * 42433 * 42473 * 42499 * 42569 * 42611 *  42689 * 42709 * 42719 * 42743 * 42751 * 42821 * 42853 * 42859 * 42863 *  42923 * 42953 * 43013 * 43049 * 43051 * 43313 * 43391 * 43403 * 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50021 * 50023 * 50051 * 50261 *  50263 * 50273 * 50411 * 50423 * 50513 * 50549 * 50591 * 50651 * 50741 *  50833 * 50873 * 50969 * 50993 * 51071 * 51203 * 51343 * 51349 * 51383 *  51427 * 51503 * 51521 * 51539 * 51577 * 51659 * 51893 * 51991 * 52069 *  52103 * 52121 * 52163 * 52289 * 52361 * 52379 * 52511 * 52553 * 52561 *  52567 * 52571 * 52583 * 52631 * 52667 * 52733 * 52813 * 52817 * 52883 *  52999 * 53051 * 53093 * 53269 * 53309 * 53411 * 53453 * 53549 * 53591 *  53639 * 53699 * 53849 * 53927 * 53951 * 54011 * 54059 * 54083 * 54091 *  54101 * 54139 * 54163 * 54193 * 54251 * 54293 * 54371 * 54401 * 54403 *  54409 * 54413 * 54443 * 54503 * 54563 * 54773 * 54779 * 54799 * 54877 *  54941 * 54959 * 55001 * 55103 * 55217 * 55229 * 55343 * 55439 * 55441 *  55469 * 55619 * 55621 * 55631 * 55633 * 55661 * 55673 * 55681 * 55721 *  55733 * 55799 * 55829 * 55889 * 55931 * 56009 * 56081 * 56087 * 56099 *  56123 * 56383 * 56393 * 56489 * 56519 * 56531 * 56663 * 56681 * 56701 *  56783 * 56843 * 56891 * 56909 * 56921 * 56951 * 56999 * 57041 * 57149 *  57203 * 57329 * 57389 * 57413 * 57773 * 57791 * 57839 * 57881 * 57901 *  58013 * 58049 * 58193 * 58211 * 58231 * 58369 * 58451 * 58511 * 58601 *  58789 * 58831 * 58889 * 58979 * 59021 * 59063 * 59077 * 59093 * 59123 *  59141 * 59341 * 59369 * 59393 * 59399 * 59453 * 59513 * 59621 * 59629 *  59723 * 59879 * 59981 * 60083 * 60101 * 60149 * 60251 * 60293 * 60331 *  60383 * 60449 * 60509 * 60689 * 60719 * 60761 * 60773 * 60779 * 61153 *  61331 * 61363 * 61409 * 61469 * 61483 * 61687 * 61703 * 61751 * 61843 *  61933 * 61961 * 61991 * 62099 * 62129 * 62137 * 62143 * 62171 * 62213 *  62233 * 62351 * 62423 * 62459 * 62501 * 62591 * 62603 * 62659 * 62753 *  62761 * 62819 * 62861 * 62981 * 62989 * 63113 * 63179 * 63313 * 63419 *  63629 * 63671 * 63743 * 63803 * 63839 * 63863 * 63929 * 64109 * 64189 *  64301 * 64373 * 64399 * 64439 * 64451 * 64627 * 64709 * 64763 * 64793 *  64853 * 64891 * 64901 * 64951 * 65003 * 65063 * 65099 * 65111 * 65119 *  65129 * 65171 * 65183 * 65309 * 65327 * 65381 * 65393 * 65447 * 65539 *  65633 * 65651 * 65843 * 65899 * 65957 * 65963 * 66029 * 66173 * 66191 *  66221 * 66293 * 66431 * 66569 * 66593 * 66701 * 66749 * 66791 * 66959 *  67043 * 67049 * 67073 * 67103 * 67121 * 67169 * 67181 * 67231 * 67349 *  67433 * 67477 * 67499 * 67559 * 67619 * 67723 * 67733 * 67801 * 67819 *  67943 * 68111 * 68171 * 68261 * 68279 * 68281 * 68489 * 68543 * 68639 *  68669 * 68699 * 68743 * 68819 * 68963 * 69029 * 69061 * 69119 * 69163 *  69191 * 69193 * 69203 * 69313 * 69341 * 69431 * 69539 * 69593 * 69763 *  69809 * 69941 * 70061 * 70079 * 70181 * 70313 * 70379 * 70589 * 70663 *  70769 * 70793 * 70853 * 70901 * 70969 * 70979 * 71153 * 71161 * 71237 *  71399 * 71453 * 71563 * 71693 * 71741 * 71843 * 71849 * 71999 * 72101 *  72161 * 72269 * 72421 * 72503 * 72623 * 72673 * 72689 * 72911 * 72949 *  73019 * 73259 * 73351 * 73421 * 73433 * 73523 * 73553 * 73589 * 73613 *  73643 * 73673 * 73709 * 73751 * 73823 * 73849 * 73951 * 74099 * 74143 *  74159 * 74201 * 74219 * 74363 * 74381 * 74471 * 74699 * 74729 * 74759 *  74771 * 74933 * 75041 * 75149 * 75161 * 75211 * 75253 * 75277 * 75289 *  75323 * 75329 * 75353 * 75389 * 75391 * 75479 * 75503 * 75629 * 75683 *  75689 * 75721 * 75821 * 75833 * 75941 * 75983 * 76001 * 76031 * 76091 *  76129 * 76259 * 76283 * 76421 * 76481 * 76579 * 76679 * 76781 * 76837 *  76871 * 76943 * 77041 * 77069 * 77101 * 77243 * 77261 * 77369 * 77383 *  77471 * 77513 * 77543 * 77587 * 77699 * 77711 * 77783 * 77813 * 77849 *  77977 * 78041 * 78059 * 78173 * 78233 * 78259 * 78311 * 78341 * 78509 *  78623 * 78653 * 78713 * 78779 * 78839 * 79039 * 79151 * 79181 * 79259 *  79283 * 79349 * 79379 * 79393 * 79411 * 79423 * 79433 * 79559 * 79589 *  79609 * 79613 * 79769 * 79811 * 79841 * 79889 * 79973 * 79999 * 80039 *  80221 * 80251 * 80309 * 80363 * 80369 * 80447 * 80473 * 80513 * 80629 *  80651 * 80669 * 80681 * 80819 * 80929 * 80933 * 81041 * 81071 * 81131 *  81281 * 81343 * 81463 * 81509 * 81563 * 81611 * 81629 * 81701 * 81839 *  81929 * 82073 * 82139 * 82193 * 82223 * 82493 * 82499 * 82529 * 82549 *  82601 * 82721 * 82759 * 82763 * 82793 * 82889 * 83243 * 83339 * 83399 *  83423 * 83459 * 83579 * 83813 * 83873 * 83939 * 83987 * 84011 * 84131 *  84229 * 84263 * 84299 * 84349 * 84391 * 84401 * 84407 * 84431 * 84443 *  84449 * 84503 * 84509 * 84533 * 84629 * 84653 * 84659 * 84713 * 84761 *  84859 * 84869 * 85009 * 85049 * 85061 * 85103 * 85121 * 85133 * 85223 *  85313 * 85411 * 85517 * 85523 * 85601 * 85639 * 85643 * 85691 * 85733 *  85793 * 85829 * 85831 * 85853 * 85931 * 86111 * 86171 * 86183 * 86291 *  86441 * 86771 * 86843 * 87049 * 87071 * 87149 * 87221 * 87299 * 87383 *  87539 * 87613 * 87701 * 87959 * 87991 * 88079 * 88223 * 88301 * 88339 *  88423 * 88463 * 88661 * 88811 * 88853 * 88919 * 89051 * 89123 * 89153 *  89213 * 89269 * 89399 * 89591 * 89603 * 89759 * 89797 * 89809 * 89909 *  89983 * 90011 * 90067 * 90089 * 90121 * 90149 * 90173 * 90281 * 90359 *  90439 * 90499 * 90599 * 90641 * 90749 * 90787 * 90803 * 90823 * 90833 *  90971 * 91079 * 91121 * 91139 * 91193 * 91249 * 91291 * 91373 * 91433 *  91463 * 91499 * 91529 * 91573 * 91583 * 91631 * 91691 * 91733 * 91841 *  92003 * 92221 * 92243 * 92251 * 92363 * 92681 * 92683 * 92723 * 92849 *  92861 * 92951 * 92993 * 93053 * 93059 * 93089 * 93113 * 93239 * 93323 *  93371 * 93479 * 93563 * 93581 * 93683 * 93893 * 93911 * 93941 * 93979 *  94079 * 94151 * 94229 * 94343 * 94421 * 94463 * 94543 * 94559 * 94573 *  94603 * 94693 * 94811 * 95143 * 95231 * 95261 * 95311 * 95393 * 95467 *  95527 * 95549 * 95561 * 95569 * 95707 * 95723 * 95731 * 95789 * 95813 *  95873 * 95891 * 95947 * 96181 * 96269 * 96293 * 96443 * 96461 * 96581 *  96601 * 96731 * 96779 * 96823 * 96851 * 96989 * 97001 * 97159 * 97241 *  97369 * 97441 * 97511 * 97523 * 97711 * 97829 * 97861 * 97871 * 97879 *  97919 * 97931 * 97943 * 98047 * 98101 * 98123 * 98143 * 98257 * 98321 *  98369 * 98453 * 98459 * 98561 * 98573 * 98621 * 98639 * 98669 * 98711 *  98849 * 98963 * 98981 * 99023 * 99041 * 99089 * 99173 * 99181 * 99251 *  99289 * 99409 * 99439 * 99551 * 99559 * 99623 * 99689 * 99761 * 99839
The abundance per 100,000 does not change from the previous exponent, but the abundance per 1,000,000 improves. This is definitely due to the way I build the exponent ...

mono patf.exe -v 3 "k" 100000
Then I tested the abundance of the d given by the program.
Result : abundance = 0.806, The same as for the former exponent j !
I also tried this entry :
mono patf.exe -v 3 "k" 1000000
Then I tested the abundance of the d given by the program.
Result : abundance = 0.898, to compare with the former abundance for the former exponent : abundance (with exponent j) = 0.877

The computer refuses to process data with entries > 10^6.
Happy (or anyone else), if you want to try, and above all, if you dare ...
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