A028372 Smallest prime that is simultaneously of forms x^2 + m*y^2 for m = 1, ..., n.

2, 2, 73, 73, 241, 241, 1009, 1009, 1009, 1009, 7561, 7561, 21961, 35281, 35281, 35281, 44641, 44641, 374089, 622561, 622561, 622561, 4379281, 4379281, 4379281, 17690689, 17690689, 17690689, 17690689, 17690689, 316234801, 1996405009, 1996405009, 1996405009

Offset: 1

Author

John L. Drost

Keywords

• nonn

Comments

Sequence A155715 lists the smallest numbers of this kind with x,y > 0, but not necessarily prime. - M. F. Hasler, Jan 27 2009

a(n) > 4*10^9 for n >= 35. - Donovan Johnson, May 29 2012

Programs

PARI

p=2; for(k=1,999, forstep( c=k,1,-1, for( b=1,sqrtint(p\c), issquare(p-c*b^2) & next(2)); p=nextprime(p+1); c=k+1); print1(p",")) \\ M. F. Hasler, Jan 27 2009

Extensions

a(17)-a(18) corrected and a(26)-a(31) from Donovan Johnson, Sep 29 2009

a(32)-a(34) from Donovan Johnson, May 29 2012