A362957 a(n) is the least prime p such that the number of distinct prime factors of p^n + 1 sets a new record.

2, 3, 5, 43, 17, 47, 151, 1697, 59, 2153, 521, 13183, 30089, 20753, 3769

Offset: 1

Author

Hugo Pfoertner, Jun 11 2023

Keywords

• nonn
• hard
• more

Comments

a(16) > 2.3*10^6; to see if there has been any progress see also A280005(16).

Crossrefs

Cf. A001221, A115973, A125137, A280005.

Programs

PARI

smallf(q,nmax) = {my(qq=q,j=0); forprime (p=2, nmax, my(k=0); while (qq%p==0, k++; qq/=p); if (k>0, j++;)); [j,qq]};
a362957(upto) = {my(nfmax=0); for (n=1, upto, forprime (p=2, oo, my(f=p^n+1, s=smallf(f,p)); if (s[1]nfmax, print1(p,", "); nfmax=nf; break)))};
a362957(12)