

A033207


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


7



7, 11, 23, 29, 37, 43, 53, 67, 71, 79, 107, 109, 113, 127, 137, 149, 151, 163, 179, 191, 193, 197, 211, 233, 239, 263, 277, 281, 317, 331, 337, 347, 359, 373, 379, 389, 401, 421, 431, 443, 449, 457, 463, 487, 491
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

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
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


REFERENCES

David A. Cox, "Primes of the Form x^2 + n y^2", Wiley, 1989.


LINKS



FORMULA

Primes congruent to {1, 7, 9, 11, 15, 23, 25} (mod 28).  T. D. Noe, Apr 29 2008


MATHEMATICA

QuadPrimes2[1, 0, 7, 10000] (* see A106856 *)


PROG



CROSSREFS



KEYWORD

nonn,easy


AUTHOR



STATUS

approved



