A380784 Prime numbers p where the cyclotomic field Q(zeta_(p-1)) has class number one.

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 61, 67, 71

Offset

1,1

Comments

For a prime number p, the cyclotomic field of power p-1 can take a significant part in Z/pZ or p-adic field Q_p, since 1~p-1 are all (p-1)-th unit roots in Z/pZ. It would be much better if the cyclotomic integer ring is a unique factorization domain.

A prime number p is in this sequence if and only if (p-1)/2 is in A005848 (if p equals 3 modulus 4) or p-1 is in A005848 (otherwise).

Primes p such that Q(chi) has class number 1 for all Dirichlet characters modulo p, where Q(chi) is the field generated by values of chi. General numbers k satisfying this condition are listed in A396476. - Jianing Song, May 27 2026

Links

Table of n, a(n) for n=1..17.

Crossrefs

Cf. A005848, A396476.

Sequence in context: A281295 A052042 A245576 * A086472 A219669 A109611

Adjacent sequences: A380781 A380782 A380783 * A380785 A380786 A380787

Keyword

nonn,fini,full

Author

Steven Lu, Feb 02 2025

Status

approved