%I
%S 4,10,25,26,34,58,65,74,82,85,106,122,145,146,169,178,185,194,202,205,
%T 218,221,226,265,274,289,298,305,314,346,362,365,377,386,394,445,458,
%U 466,481,482,485,493,505,514,533,538,545,554,562,565,586,626,629,634
%N Pythagorean semiprimes: products of two Pythagorean primes (A002313).
%C Fermat's 4n+1 theorem, sometimes called Fermat's twosquare theorem or simply "Fermat's theorem," states that a prime number p can be represented in an essentially unique manner (up to the order of addends) in the form x^2 + y^2 for integer x and y iff p = 1 (mod 4) or p = 2 (which is a degenerate case with x = y = 1). The theorem was stated by Fermat, but the first published proof was by Euler.
%D Conway, J. H. and Guy, R. K. The Book of Numbers. New York: SpringerVerlag, pp. 146147 and 220223, 1996.
%D Hardy, G. H. and Wright, E. M. An Introduction to the Theory of Numbers, 5th ed. Oxford, England: Clarendon Press, pp. 13 and 219, 1979.
%D Seroul, R. "Prime Number and Sum of Two Squares." Section 2.11 in Programming for Mathematicians. Berlin: SpringerVerlag, pp. 1819, 2000.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Fermats4nPlus1Theorem.html">Fermat's 4n Plus 1 Theorem.</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Semiprime.html">Semiprime.</a>
%F {a(n)} = {p*q: p and q both elements of A002313} = {p*q: p and q both of form m^2 + n^2 for integers m, n}.
%Y Cf. A001358, A002313, A002330, A002331.
%K easy,nonn
%O 1,1
%A _Jonathan Vos Post_, Jun 12 2005
