A243402 Primes p such that p^10 - p^9 - p^8 - p^7 - p^6 - p^5 - p^4 - p^3 - p^2 - p - 1 is prime.

449, 839, 857, 941, 977, 1109, 1289, 1607, 1901, 2591, 2711, 3041, 3299, 4007, 4349, 4721, 5531, 5849, 6311, 6779, 6911, 7451, 7829, 7907, 8369, 8597, 8999, 9419, 9767, 11351, 12917, 13421, 14321, 14969, 15077, 15131, 15227, 15551, 15809, 16649, 16979, 17021, 17291, 17417

Offset: 1

Author

Derek Orr, Jun 04 2014

Keywords

• nonn

Comments

No terms end in a 3, since if p == 3 (mod 10), then p^10 - p^9 - p^8 - p^7 - p^6 - p^5 - p^4 - p^3 - p^2 - p - 1 == 5 (mod 10) and is therefore not prime. - Michel Marcus, Jun 25 2014

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..11323

Crossrefs

Cf. A243318.

Programs

Mathematica

Select[Prime[Range[2100]],PrimeQ[#^10-Total[#^Range[9]]-1]&] (* Harvey P. Dale, Sep 08 2019 *)

PARI

for(n=1,5*10^4,if(ispseudoprime(n)&&ispseudoprime(n^10-sum(i=0,9,n^i)),print1(n,", ")))

Python

import sympy
from sympy import isprime
{print(n,end=', ') for n in range(5*10**4) if isprime(n**10-n**9-n**8-n**7-n**6-n**5-n**4-n**3-n**2-n-1) and isprime(n)}