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

Author

Steven Lu, Feb 02 2025

Keywords

• nonn
• fini
• full

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).

Crossrefs

Cf. A005848.