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Primes p with property that p^2 is of the form x^2 + 40y^2.
3

%I #27 Sep 20 2024 06:10:58

%S 7,11,13,19,23,37,41,47,53,59,89,103,127,131,139,157,167,173,179,197,

%T 211,223,241,251,263,277,281,293,317,331,367,373,379,383,397,401,409,

%U 419,449,463,487,491,499,503,521,557,569,571,601,607,613,619,641,647

%N Primes p with property that p^2 is of the form x^2 + 40y^2.

%C All p^2 are congruent to {1, 9} (mod 40), as in A107145.

%C Rational primes that decompose in the field Q(sqrt(-10)). - _N. J. A. Sloane_, Dec 26 2017

%H Robert Price, <a href="/A155488/b155488.txt">Table of n, a(n) for n = 1..1000</a>

%H Zak Seidov, <a href="http://zak08.livejournal.com/4251.html">First 1000 terms</a>

%H <a href="/index/Pri#primes_decomp_of">Index to sequences related to decomposition of primes in quadratic fields</a>

%p Load the Maple program HH given in A296920. Then run HH(-10, 200); This produces A155488, A296925, A293859. - _N. J. A. Sloane_, Dec 26 2017

%Y Cf. A107145 (Primes of the form x^2 + 40y^2).

%K nonn

%O 1,1

%A _Zak Seidov_, Jan 23 2009