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A107961 Pythagorean semiprimes: products of two Pythagorean primes (A002313). 0


%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 two-square 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: Springer-Verlag, pp. 146-147 and 220-223, 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: Springer-Verlag, pp. 18-19, 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

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Last modified June 6 17:28 EDT 2020. Contains 334830 sequences. (Running on oeis4.)