A355965 Primes p such that (p+10)^(p-1) == 1 (mod p^2).

13, 41, 97, 809, 1151, 1657, 800011

Offset: 1

Author

Felix Fröhlich, Jul 21 2022

Keywords

• nonn
• hard
• more

Comments

A computer search taking less than 3 seconds shows there are no further terms below the one millionth prime. - Harvey P. Dale, Mar 04 2024

I ran the PARI program below for 8.5 hours and it did not find any further terms. (I do not know how far it searched.) - N. J. A. Sloane, Mar 05 2024

Crossrefs

(p+k)^(p-1) == 1 (mod p^2): A355959 (k=2), A355960 (k=5), A355961 (k=6), A355962 (k=7), A355963 (k=8), A355964 (k=9).

Programs

Mathematica

Select[Prime[Range[70000]],PowerMod[#+10,#-1,#^2]==1&] (* Harvey P. Dale, Mar 04 2024 *)

PARI

forprime(p=1, , if(Mod(p+10, p^2)^(p-1)==1, print1(p, ", ")))