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 A176969 Numbers n such that n^2 + 13^2 is prime. 5

%I

%S 2,8,10,12,20,22,28,30,32,38,42,48,58,60,62,68,80,90,100,108,110,112,

%T 122,128,138,142,148,150,168,172,180,190,198,200,202,210,228,230,232,

%U 238,242,248,258,262,268,280,282,302,310,318,340,342,360,362,368,378

%N Numbers n such that n^2 + 13^2 is prime.

%C The n^2 + d conjecture is a famous and still unsolved problem.

%C It states that there exist an infinite number of primes whose values are of the form n^2 + d for some integer n.

%C This is case d = 13^2.

%D J. Matousek, J. Nesetril: Diskrete Mathematik: eine Entdeckungsreise, Springer-Lehrbuch, 2. Aufl., Berlin, 2007

%D M. du Sautoy: Die Musik der Primzahlen: Auf den Spuren des groessten Raetsels der Mathematik, Deutscher Taschenbuch Verlag, 2006

%e 2^2 + 13^2 = 173 = prime(40), 2 is first term.

%e 12^2 + 13^2 = 313 = prime(65) = palprime(11), 12 is 4th term.

%e 310^2 + 13^2 = 96269 = prime(9274) = palprime(106), 310 the 49th term.

%o (PARI) isok(n) = isprime(n^2 + 13^2) \\ _Michel Marcus_, Jun 28 2013

%Y Cf. A000040, A000290, A056899, A113536, A176371.

%K nonn

%O 1,1

%A Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Apr 29 2010

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Last modified April 20 03:02 EDT 2021. Contains 343121 sequences. (Running on oeis4.)