A084163 - OEIS

%I #6 Apr 15 2014 01:14:32

%S 29,41,197,229,269,2617,2729,2897,4649,37201,37277,169553,170081,

%T 170873,282577,9491309,9493889,15614761,69955373,69955577,115195429,

%U 115196129,312316481,513773717,846651233,3778288373,3778289381,3778290641

%N Primes which are -1 mod m, where m is the index of the prime in sequence A002313 (Real primes with corresponding complex primes). The index m can be found in A084164 Primes which are 1 mod m can be found in sequence A084165.

%C Real primes 2,5,13,17,29,37,... have a unique representation as sum of two squares. Values larger 2 are the primes p with p = 1 mod 4. This is sequence A002313. If p = x^2 + y^2, the corresponding complex prime is x+y*i. First complex prime is 1+i with 2 as corresponding real prime, according to reference, page 1-2.

%D Handbook of First Complex Prime Numbers, Part1+2 Ervand Kogbetliantz and Alice Krikorian, Gordon and Breach, 1971. The list in Part 2 contains an error: on page 919, column 2, number 5 is printed twice, so the indices after that number are wrong.

%e 197 is the 22nd prime in sequence A002313, 22*9 = 198, so 197 = -1 mod 22.

%Y Cf. A002313, A084164, A084165.

%K nonn

%O 1,1

%A _Sven Simon_, May 17 2003