The Top Twenty--a Prime Page Collection

Woodall Primes

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The Prime Pages keeps a list of the 5000 largest known primes, plus a few each of certain selected archivable forms and classes. These forms are defined in this collection's home page. This page is about one of those forms. Comments and suggestions requested.

(up) Definitions and Notes

A Woodall prime is any prime of the form n.2n-1 (compare with the Cullen primes). The Woodall primes with n < 30000 are those with n = 2, 3, 6, 30, 75, 81, 115, 123, 249, 362, 384, 462, 512, 751, 822, 5312, 7755, 9531, 12379, 15822, and 18885. It is conjectured that there are infinitely many Woodall primes.

A prime of the form n.bn-1 with b not 2, is a generalized Woodall prime.

(up) Record Primes of this Type

rankprime digitswhowhencomment
1938237 · 23752950 - 1 1129757 L521 Dec 2007 Woodall
21183953 · 22367907 - 1 712818 L447 Sep 2007 Woodall
3251749 · 22013995 - 1 606279 L436 Aug 2007 Woodall
41467763 · 21467763 - 1 441847 L381 Jun 2007 Woodall
51268979 · 21268979 - 1 382007 L201 Jan 2007 Woodall
61195203 · 21195203 - 1 359799 L124 Jul 2005 Woodall
7667071 · 2667071 - 1 200815 g55 Sep 2000 Woodall
8151023 · 2151023 - 1 45468 g25 May 1998 Woodall
971509 · 2143019 - 1 43058 g23 Apr 1998 Woodall, arithmetic progression (2, d=(143018 · 283969 - 80047) · 259049) [x12]
1049363 · 298727 - 1 29725 Y May 1997 Woodall
1123005 · 223005 - 1 6930 Y May 1997 Woodall
1222971 · 222971 - 1 6920 Y May 1997 Woodall
1318885 · 218885 - 1 5690 K Dec 1987 Woodall
147911 · 215823 - 1 4768 K Dec 1987 Woodall
1512379 · 212379 - 1 3731 K Dec 1984 Woodall
169531 · 29531 - 1 2874 K Dec 1984 Woodall
177755 · 27755 - 1 2339 K Dec 1984 Woodall
1883 · 25318 - 1 1603 K Dec 1984 Woodall

(up) Related Pages

(up) References

CW17
A. J. C. Cunningham and H. J. Woodall, "Factorisation of Q=(2q ± q) and q*2q ± 1," Math. Mag., 47 (1917) 1--38. [A classic paper in the history of the study of Cullen numbers. See also [Keller95]]
Karst73
E. Karst, Prime factors of Cullen numbers n· 2n± 1.  In "Number Theory Tables," A. Brousseau editor, Fibonacci Assoc., 1973.  San Jose, CA, pp. 153--163,
Keller95
W. Keller, "New Cullen primes," Math. Comp., 64 (1995) 1733-1741.  Supplement S39-S46.  MR 95m:11015
Ribenboim95 (p. 360-361)
P. Ribenboim, The new book of prime number records, 3rd edition, Springer-Verlag, New York, NY, 1995.  pp. xxiv+541, ISBN 0-387-94457-5. MR 96k:11112 [An excellent resource for those with some college mathematics. Basically a Guinness Book of World Records for primes with much of the relevant mathematics. The extensive bibliography is seventy-five pages.]
Riesel69a
H. Riesel, "Lucasian criteria for the primality of N = h · 2n - 1," Math. Comp., 23:108 (1969) 869--875.  MR 41:6773
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