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

Author

N. J. A. Sloane, Nov 06 2013

Keywords

• nonn

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

• 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.