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A355965
Primes p such that (p+10)^(p-1) == 1 (mod p^2).
6
13, 41, 97, 809, 1151, 1657, 800011
OFFSET
1,1
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
MATHEMATICA
Select[Prime[Range[70000]], PowerMod[#+10, #-1, #^2]==1&] (* Harvey P. Dale, Mar 04 2024 *)
PROG
(PARI) forprime(p=1, , if(Mod(p+10, p^2)^(p-1)==1, print1(p, ", ")))
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).
Sequence in context: A167585 A141970 A305155 * A231885 A167240 A147247
KEYWORD
nonn,hard,more
AUTHOR
Felix Fröhlich, Jul 21 2022
STATUS
approved