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