A230869 Primes p such that the class number h-tilde_p^{+} of the real cyclotomic field Q(zeta_p + zeta_p^(-1)) is greater than 1.

163, 191, 229, 257, 277, 313, 349, 397, 401, 457, 491, 521, 547, 577, 607, 631, 641, 709, 733, 761, 821, 827, 829, 853, 857, 877, 937, 941, 953, 977, 1009, 1063, 1069, 1093, 1129, 1153, 1229, 1231, 1297, 1373, 1381, 1399, 1429, 1459, 1489, 1567, 1601, 1697, 1699, 1777, 1789, 1831, 1861, 1873, 1879, 1889, 1901, 1951

Offset

1,1

Comments

Taken from the "Main Table" of Schoof.

There is a very slight chance that some primes are missing. In the unlikely event that the number that Schoof calls h-tilde_p is 1, while the actual class number h_p is actually not equal to 1, the prime p would be missing (see the Schoof and Miller articles for details).

Links

Table of n, a(n) for n=1..58.

John C. Miller, Class numbers of totally real fields and applications to the Weber class number problem, arXiv:1405.1094 [math.NT], 2014.

John C. Miller, Real cyclotomic fields of prime conductor and their class numbers, arXiv:1407.2373 [math.NT], 2014.

Rene Schoof, Class numbers of real cyclotomic fields of prime conductor, Math. Comp., 72 (2002), 913-937.

Crossrefs

Cf. A230870 (for the actual class numbers).

See also A000927, A055513, A035113, A035114, A035115.

Sequence in context: A057604 A243532 A272984 * A132250 A303379 A142940

Adjacent sequences: A230866 A230867 A230868 * A230870 A230871 A230872

Keyword

nonn

Author

N. J. A. Sloane, Nov 06 2013

Status

approved