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

Author

K. D. Bajpai, Jun 06 2014

Keywords

• nonn

Comments

Each term in the sequence yields, by definition, a pair of twin primes. The first term 31 results in 858874531 and 858874529, which are twin primes.

Intersection of A243471 and A243472.

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

Crossrefs

Cf. A000040, A001097, A001359, A006512, A238136.

Programs

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);

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}];