A243522 Primes p such that p^6 - p^5 + 1 and p^6 - p^5 - 1 are both primes.
31, 181, 1039, 4591, 13687, 21589, 30211, 40771, 41641, 41947, 55441, 56437, 63559, 70867, 81307, 83407, 83869, 87649, 91639, 111229, 126199, 126499, 134287, 157999, 189559, 201307, 214129, 220699, 225751, 228559, 251431, 281557, 289717, 290839, 323767, 337639
Offset: 1
Keywords
Examples
31 is prime and appears in the sequence because [31^6 -31^5 + 1 = 858874531] and [31^6 -31^5 - 1 = 858874529] are both primes. 181 is prime and appears in the sequence because [181^6 -181^5 + 1 = 34967564082181] and [181^6 -181^5 - 1 = 34967564082179] are both primes.
Links
- K. D. Bajpai, Table of n, a(n) for n = 1..1785
Programs
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Maple
A243522 := proc() local a,b,d; a:=ithprime(n); b:= a^6-a^5+1; d:= a^6-a^5-1; if isprime (b)and isprime (d) then RETURN (a); fi; end: seq(A243522 (), n=1..30000);
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Mathematica
c = 0; a = 2; Do[k = Prime[n]; If[PrimeQ[k^6 - k^5 + 1] && PrimeQ[k^6 - k^5 - 1], c++; Print[c, " ", k]], {n, 1, 2000000}];
Comments