A121834 Primes p of the form 4*n^2 + 1 such that 4*p^2+1 is also prime.

5, 37, 677, 1297, 2917, 8837, 13457, 50177, 147457, 156817, 246017, 341057, 414737, 746497, 1136357, 1726597, 1833317, 2119937, 2802277, 2808977, 3013697, 3549457, 3865157, 3896677, 4104677, 4384837, 5354597, 5410277, 5779217, 6031937, 6635777, 7001317

Offset: 1

Author

Zak Seidov, Aug 28 2006

Keywords

• nonn

Comments

Intersection of A001912 and A121326. Except for the first term all other terms are == 7 (mod 10). Also all the primes 4*p^2+1 are == 7 (mod 10). - Zak Seidov, Mar 05 2015

Crossrefs

Cf. A002496, A052291, A121326.

Programs

Mathematica

fpQ[n_]:=PrimeQ[n]&&PrimeQ[4n^2+1]; Select[4Range[2000]^2+1,fpQ] (* Harvey P. Dale, Nov 07 2016 *)

PARI

isA121834(n)={ if( (n-1) %4, return(0) ; ) ; if( issquare((n-1)/4), if( isprime(4*n^2+1), return(1), return(0) ), return(0) ; ) ; } { for(i=1,1000000, p=prime(i) ; if( isA121834(p), print1(p,",") ; ) ; ) ; } /* R. J. Mathar, Sep 01 2006*/

Extensions

More terms from R. J. Mathar, Sep 01 2006