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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

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