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%I #18 May 28 2026 19:32:31
%S 2,3,5,7,11,13,17,19,23,29,31,37,41,43,61,67,71
%N Prime numbers p where the cyclotomic field Q(zeta_(p-1)) has class number one.
%C 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.
%C 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).
%C 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
%Y Cf. A005848, A396476.
%K nonn,fini,full
%O 1,1
%A _Steven Lu_, Feb 02 2025