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Smallest prime that is simultaneously of forms x^2 + m*y^2 for m = 1, ..., n.
4

%I #14 Jul 04 2018 15:49:25

%S 2,2,73,73,241,241,1009,1009,1009,1009,7561,7561,21961,35281,35281,

%T 35281,44641,44641,374089,622561,622561,622561,4379281,4379281,

%U 4379281,17690689,17690689,17690689,17690689,17690689,316234801,1996405009,1996405009,1996405009

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

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

%C a(n) > 4*10^9 for n >= 35. - _Donovan Johnson_, May 29 2012

%o (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

%K nonn

%O 1,1

%A _John L. Drost_

%E a(17)-a(18) corrected and a(26)-a(31) from _Donovan Johnson_, Sep 29 2009

%E a(32)-a(34) from _Donovan Johnson_, May 29 2012