> Michael Shafer discovered the 40th known Mersenne prime, 2^20996011-1. Am I too late to congratulate with Michael, George, Scott and you all for this result? Very well done!
Sincerely, Paolo p.fani @ infogroup.it p.s. as an amusement, have a look at the digit distribution of such prime, compared with that of an equal amount of decimals from gamma, e and pi. Last column is delta with expected average for a random distribution. 2^20996011-1 0: 631705 9,994652% -338 1: 632720 10,010711% +677 2: 630989 9,983324% -1054 3: 631467 9,990887% -576 4: 632004 9,999383% -39 5: 633283 10,019619% +1240 6: 630929 9,982375% -1114 7: 633503 10,023100% +1460 8: 632964 10,014572% +921 9: 630866 9,981378% -1177 -------- 6320430 mean: 632043 ± 1008,880 = 632043 ± 0,159622% (n-1) mean: 632043 ± 957,108 = 632043 ± 0,151431% (n) -------------------------------------------------- gamma(6320430) 0: 631692 9,994447% -351 1: 631788 9,995965% -255 2: 632064 10,000332% +21 3: 632594 10,008718% +551 4: 632435 10,006202% +392 5: 633459 10,022404% +1416 6: 631379 9,989494% -664 7: 631295 9,988165% -748 8: 631961 9,998703% -82 9: 631763 9,995570% -280 -------- 6320430 mean: 632043 ± 644,335 = 632043 ± 0,101945% (n-1) mean: 632043 ± 611,270 = 632043 ± 0,096713% (n) -------------------------------------------------- e(6320430) 0: 631149 9,985855% -894 1: 633197 10,018258% +1154 2: 630780 9,980017% -1263 3: 633443 10,022150% +1400 4: 632955 10,014429% +912 5: 632294 10,003971% +251 6: 631789 9,995981% -254 7: 632132 10,001408% +89 8: 630789 9,980160% -1254 9: 631902 9,997769% -141 -------- 6320430 mean: 632043 ± 957,178 = 632043 ± 0,151442% (n-1) mean: 632043 ± 908,058 = 632043 ± 0,143670% (n) -------------------------------------------------- pi(6320430) 0: 631536 9,991978% -507 1: 632438 10,006250% +395 2: 631748 9,995333% -295 3: 631940 9,998370% -103 4: 632319 10,004367% +276 5: 631942 9,998402% -101 6: 630422 9,974353% -1621 7: 632985 10,014904% +942 8: 632241 10,003133% +198 9: 632859 10,012911% +816 -------- 6320430 mean: 632043 ± 731,600 = 632043 ± 0,115752% (n-1) mean: 632043 ± 694,057 = 632043 ± 0,109812% (n) -------------------------------------------------- Finally, of course, the biggest perfect (delta rounded to the nearest integer) (2^20996011-1)*2^20996010 0: 1265474 10,010982% +1388 1: 1263035 9,991687% -1051 2: 1263218 9,993135% -868 3: 1265979 10,014977% +1893 4: 1264223 10,001085% +137 5: 1262192 9,985018% -1894 6: 1264569 10,003823% +483 7: 1263798 9,997723% -288 8: 1263617 9,996291% -469 9: 1264753 10,005278% +667 -------- 12640858 mean: 1264085,8 ± 1152,539 = 1264085,8 ± 0,0911757% (n-1) mean: 1264085,8 ± 1093,394 = 1264085,8 ± 0,0864968% (n) _________________________________________________________________________ Unsubscribe & list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
