cp's OEIS Frontend

A033207 Primes of the form x^2 + 7*y^2.

%I A033207 #52 Nov 03 2023 07:58:25
%S A033207 7,11,23,29,37,43,53,67,71,79,107,109,113,127,137,149,151,163,179,191,
%T A033207 193,197,211,233,239,263,277,281,317,331,337,347,359,373,379,389,401,
%U A033207 421,431,443,449,457,463,487,491
%N A033207 Primes of the form x^2 + 7*y^2.
%C A033207 Except for a(1) = 7, these are the primes which can be written in the form a^2 + 7*b^2 with a > 0 and b > 0. - _V. Raman_, Sep 08 2012
%C A033207 These are the primes p for which p^3 - 1 is divisible by 7, with two exceptions: p = 2 is not in the sequence even though 2^3 - 1 is divisible by 7, and p = 7 is in the sequence even though 7^3 - 1 is not divisible by 7. Except for p = 7, if p^3 - 1 is not divisible by 7, it is congruent to 5 (mod 7). - _Richard R. Forberg_, Jun 03 2013
%D A033207 David A. Cox, "Primes of the Form x^2 + n y^2", Wiley, 1989.
%H A033207 Ray Chandler, <a href="/A033207/b033207.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from T. D. Noe)
%H A033207 Sushma Palimar and B. R. Shankar, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL15/Palimar/palimar5.html">Mersenne Primes in Real Quadratic Fields</a>, Journal of Integer Sequences, Vol. 15 (2012), #12.5.6.
%H A033207 N. J. A. Sloane et al., <a href="https://oeis.org/wiki/Binary_Quadratic_Forms_and_OEIS">Binary Quadratic Forms and OEIS</a> (Index to related sequences, programs, references)
%F A033207 Primes congruent to {1, 7, 9, 11, 15, 23, 25} (mod 28). - _T. D. Noe_, Apr 29 2008
%t A033207 QuadPrimes2[1, 0, 7, 10000] (* see A106856 *)
%o A033207 (PARI) is(n)=kronecker(n,7)>=0 && isprime(n) && n>2 \\ _Charles R Greathouse IV_, Nov 19 2012
%Y A033207 Essentially the same as A045373. Primes in A020670.
%Y A033207 Cf. A002344, A002345, A139643.
%K A033207 nonn,easy
%O A033207 1,1
%A A033207 _N. J. A. Sloane_