Woodall Primes

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.

(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
18508301 · 217016603 - 1 5122515 L4784 Mar 2018 Woodall
2938237 · 23752950 - 1 1129757 L521 Dec 2007 Woodall
31183953 · 22367907 - 1 712818 L447 Sep 2007 Woodall
4251749 · 22013995 - 1 606279 L436 Aug 2007 Woodall
51467763 · 21467763 - 1 441847 L381 Jun 2007 Woodall
61268979 · 21268979 - 1 382007 L201 Jan 2007 Woodall
71195203 · 21195203 - 1 359799 L124 Jul 2005 Woodall
8667071 · 2667071 - 1 200815 g55 Sep 2000 Woodall
9151023 · 2151023 - 1 45468 g25 May 1998 Woodall
1071509 · 2143019 - 1 43058 g23 Apr 1998 Woodall, arithmetic progression (2, d=(143018 · 283969 - 80047) · 259049) [x12]
1149363 · 298727 - 1 29725 Y May 1997 Woodall
1223005 · 223005 - 1 6930 Y May 1997 Woodall
1322971 · 222971 - 1 6920 Y May 1997 Woodall
1418885 · 218885 - 1 5690 K Dec 1987 Woodall
157911 · 215823 - 1 4768 K Dec 1987 Woodall
1612379 · 212379 - 1 3731 K Dec 1984 Woodall
179531 · 29531 - 1 2874 K Dec 1984 Woodall
187755 · 27755 - 1 2339 K Dec 1984 Woodall
1983 · 25318 - 1 1603 K Dec 1984 Woodall

(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., San Jose, CA, 1973.  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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