A092901 - OEIS

%I #26 Mar 05 2019 18:17:02

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

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

%C 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.

%C Corrected using latest data from Buhler and Harvey. - _T. D. Noe_, Apr 27 2011

%H J. Buhler, R. Crandall, R. Ernvall, T. Metsankyla and M. A. Shokrollahi, <a href="http://dx.doi.org/10.1006/jsco.1999.1011">Irregular Primes and Cyclotomic Invariants to 12 Million</a>, J. Symbolic Computation 31, 2001, 89-96.

%H Joe Buhler and David Harvey, <a href="http://arxiv.org/abs/0912.2121">Irregular primes to 163 million</a>, arXiv:0912.2121 [math.NT], 2009.

%H Joe Buhler and David Harvey, <a href="http://web.maths.unsw.edu.au/~davidharvey/papers/irregular/">Irregular primes to 163 million</a>

%H William Hart, David Harvey and Wilson Ong, <a href="https://doi.org/10.1090/mcom/3211">Irregular primes to two billion</a>, Mathematics of Computation, Vol. 86, No. 308 (2017), pp. 3031-3049; also available at <a href="https://arxiv.org/abs/1605.02398">arXiv:1605.02398 [math.NT]</a>, 2016.

%H David Harvey, <a href="https://web.maths.unsw.edu.au/~davidharvey/papers/twobillion/">Irregular primes to two billion</a> (includes a list of all primes less than 2^31).

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/IrregularPrime.html">Irregular Prime</a>

%e The smallest irregular prime is 37.

%Y Cf. A000928.

%K nonn,more,hard

%O 1,2

%A _Eric W. Weisstein_, Mar 13 2004

%E a(6) and a(7) from _T. D. Noe_, Mar 31 2004

%E a(8) from _T. D. Noe_, Apr 27 2011

%E a(9) from _Amiram Eldar_, Mar 05 2019