About site: Math/Number Theory/Prime Numbers - Generalized Woodall Numbers

About site: http://science.kennesaw.edu/~jdemaio/generali.htm

Title: Math/Number Theory/Prime Numbers - Generalized Woodall Numbers An organized search for primes of the form n*b^n-1.

Hardy-Littlewood_Constants Infinite series over primes are the main topic in Hadamard-de la Vallée Poussin constants and in Brun's constant.

Henri_Lifchitz Research in number theory, prime numbers and parity of arithmetic functions. Includes primality testing theorems and prime number chains. In English and French.

Introduction_to_Twin_Primes_and_Brun\'s_Constant An article by Pascal Sebah with the results of computation of the twin primes up to 5.10^15.

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Generalized Woodall Numbers A Woodall number is a number of the form

. A Woodall prime is any prime number of the same form. This notion can be generalized to numbers of the form

where

. The following is a list of generalized Woodall primes. Initially primes were discovered using the program Primeform, developed by Chris Nash and most primes below with an exponent less than 1000 are probable primes. Primality tests will be run on all such values in the future. A primality test has been run on all primes with an exponent of 1000 or greater. Yves Gallot has added a primality test for generalized Woodall primes to version 5.6 of Proth. The checked column indicates the maximum exponent checked for the given base b. Similarly, the reserved column indicates the maximum exponent reserved for the given base b. Currently, the most common checked value is 9000 and the reserved value is 9000 for all bases b unless otherwise noted in the chart below. Please email me at jdemaio@kennesaw.edu if you wish to assist in this search for generalized Woodall primes. This page was last updated on Sunday, November 11, 2001. b n Checked Reserved 3 2,6,10,18,40,46,86,118,170,1172,1698,1810,2268, 4338,18362,72662,113570 113570 113570 4 3,5,8,14,23,63,107,132,428,530,1137,1973,2000,7064, 20747,79574 80000 80000 5 8,14,42,384,564,4256,6368,15400,21132,27180 30170 30170 6 19,20,24,34,77,107,114,122,165,530,1999,4359,11842 12059,13802, 22855 36000 36000 7 18,68,84,3812,12380,14838 35000 35000 8 7,12,25,44,219,252,507,1155,2259,2972,4584,12422,13905 59000 70000 9 10,58,264,1568,4198,10063 20000 30000 10 11,15,39,60,72,77,117,183,252,396,1745,2843,4665,5364 20300 25000 11 252,1184,1308, 15000 25000 12 43,175,821,910,1157, 13748 14000 25000 13 50000 50000 14 98,104,128,180,834,1633,8000 18600 25000 15 14,2312,16718 22750 25000 16 167,189,639 21000 25000 17 18,20,38,68,3122,3488, 20800 25000 18 28,30,39,45,112,348,380,458,585 25000 19 410 14000 25000 20 44,60,80,123,429,1166,2065,8774 15900 25000 21 200,282,294,1174,2492,4348 16100 25000 22 140,158,263,795,992 12000 25000 23 18000 25000 24 124,1483 11800 25000 25 68,104,450 10250 25000 26 79,132,243,373,720,1818,11904 17000 25000 27 2420,6638 10000 25000 28 47,71,624,1149,2399,8048 12300 25000 29 10400 25000 30 63,331,366,1461,3493,4002,5940,13572 17500 25000 31 2454 9000 12000 32 140,180,726,799 13316 33 42,1032,3408 15000 15000 34 164,530,984,3560 16896 16896 35 38,132,1248,3270,6900 16914 16914 36 62,198,972,1007,3154,4100,14749 15000 15000 37 740,978,11046 15000 15000 38 67,85,139,211,1231,2293,3451 14759 39 448,2848 9000 40 51,99,158,686,836 9000 41 84,390,2238 15079 42 135,310,850,1282,7342 9000 43 15000 44 43,55 9000 45 84,94,168,700,1204 9000 46 140,287 9000 47 140,348,780 9000 48 115,127,525,1284,1313 9000 49 710,7674 9000 50 2390,2527 9000 51 9000 52 261,270,450 9000 53 60,110 9000 54 72,293,353,7524 9000 55 2064,7950 9000 56 414,663,1494,3692 9000 57 468,846,3422,3812 9000 58 168,440,1139,1709,2285 9000 59 890,1554 9000 60 123,294,765,1474,1954,4182,7540 9000 61 362,1824 9000 62 3099 9000 63 318 9000 64 357,402 9000 65 1776,3170 9000 66 210,6323 9000 67 80 9000 68 141,4452 9000 69 9000 70 285,984,1085,1223,2468,5286 9000 71 192 9000 72 102,222,295,778,1449,2721,2985,6492 9000 73 140,218,362 12000 74 7202 9000 75 9000 76 113,248 9000 77 504 9000 78 160,385,391,1225,1666,6669 9000 79 3024 9000 80 2817 9000 81 270,508 9000 82 81,10025 12000 83 858 12000 84 282,1241,6130 12000 85 116 12000 86 1479 12000 87 240,5826 12000 88 1499 12000 89 824,2754,8078 12000 90 130,371,516 12000 91 960 12000 92 289,315,1922,8678 12000 93 138,184,344 12000 94 338,485,623,4655,5805,10514 17177 95 98,348,686 12000 96 113,1030,4187,8388 12000 97 182,572 12000 98 108,5708,7209 12000 99 12000 100 471 12000 Contributors Dirk Augustin, Ray Ballinger, Joe DeMaio, Yves Gallot, Steven Harvey, Kimmo Herranen, Yary Hluchan, Peter Nemeth, Jose Manuel Plaza, Pavlos Saridis, Jason Zaruba

An	organized	search	for
primes	of	the	form	n*b^n-1.

http://science.kennesaw.edu/~jdemaio/generali.htm

Generalized Woodall Numbers 2008 November

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An organized search for primes of the form n*b^n-1.

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