A092901 Number of irregular primes (A000928) less than 10^n.

0, 3, 64, 497, 3789, 30870, 261871, 2266482, 20006269

Offset

1,2

Comments

Buhler maintains a list of regular and irregular primes. Data about each irregular prime includes the index of irregularity, irregular pairs, Vandiver residue and two cyclotomic residues.

Corrected using latest data from Buhler and Harvey. - T. D. Noe, Apr 27 2011

Links

Table of n, a(n) for n=1..9.

J. Buhler, R. Crandall, R. Ernvall, T. Metsankyla and M. A. Shokrollahi, Irregular Primes and Cyclotomic Invariants to 12 Million, J. Symbolic Computation 31, 2001, 89-96.

Joe Buhler and David Harvey, Irregular primes to 163 million, arXiv:0912.2121 [math.NT], 2009.

Joe Buhler and David Harvey, Irregular primes to 163 million

William Hart, David Harvey and Wilson Ong, Irregular primes to two billion, Mathematics of Computation, Vol. 86, No. 308 (2017), pp. 3031-3049; also available at arXiv:1605.02398 [math.NT], 2016.

David Harvey, Irregular primes to two billion (includes a list of all primes less than 2^31).

Eric Weisstein's World of Mathematics, Irregular Prime

Example

The smallest irregular prime is 37.

Crossrefs

Cf. A000928.

Sequence in context: A175985 A037108 A249097 * A099338 A289668 A119924

Adjacent sequences: A092898 A092899 A092900 * A092902 A092903 A092904

Keyword

nonn,more,hard

Author

Eric W. Weisstein, Mar 13 2004

Extensions

a(6) and a(7) from T. D. Noe, Mar 31 2004

a(8) from T. D. Noe, Apr 27 2011

a(9) from Amiram Eldar, Mar 05 2019

Status

approved