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%I #18 Mar 05 2019 16:24:36
%S 491,617,647,1151,1217,1811,1847,2939,3833,4003,4657,4951,6763,7687,
%T 8831,9011,10463,10589,12073,13217,14533,14737,14957,15287,15787,
%U 15823,16007,17681,17863,18713,18869,20533,20939,24019,24659,25153,26561
%N Irregular primes with irregularity index three.
%H Amiram Eldar, <a href="/A060975/b060975.txt">Table of n, a(n) for n = 1..10000</a> (calculated by Hart et al., terms 1..9824 from T. D. Noe, calculated by Buhler et al.)
%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 <a href="/index/Be#Bernoulli">Bernoulli numbers, irregularity index of primes</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).
%t Do[p = Prime[n]; k = 1; c = 0; While[ 2*k < p - 3, If[ Mod[ Numerator[ BernoulliB[2*k]], p] == 0, c++ ]; k++ ]; If[ c == 3, Print[p]], {n, 3, 1000} ]
%t Do[p = Prime@n; k = 1; c = 0; While[ 2*k < p - 3, If[ Mod[ Numerator[ BernoulliB[2*k]], p] == 0, c++ ]; k++ ]; If[ c == 3, Print@p], {n, 3, 13887} ]
%Y Cf. A000928, A000367, A060974, A060975, A073276 and A073277.
%K nonn
%O 1,1
%A _Robert G. Wilson v_, Jul 22 2002
%E Extended by _Robert G. Wilson v_, Sep 20 2006
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