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A060975
Irregular primes with irregularity index three.
13
491, 617, 647, 1151, 1217, 1811, 1847, 2939, 3833, 4003, 4657, 4951, 6763, 7687, 8831, 9011, 10463, 10589, 12073, 13217, 14533, 14737, 14957, 15287, 15787, 15823, 16007, 17681, 17863, 18713, 18869, 20533, 20939, 24019, 24659, 25153, 26561
OFFSET
1,1
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000 (calculated by Hart et al., terms 1..9824 from T. D. Noe, calculated by Buhler et al.)
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.
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).
MATHEMATICA
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} ]
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} ]
CROSSREFS
KEYWORD
nonn
AUTHOR
Robert G. Wilson v, Jul 22 2002
EXTENSIONS
Extended by Robert G. Wilson v, Sep 20 2006
STATUS
approved