

A033210


Primes of the form x^2+13*y^2.


13



13, 17, 29, 53, 61, 101, 113, 157, 173, 181, 233, 257, 269, 277, 313, 337, 373, 389, 433, 521, 569, 601, 641, 653, 673, 677, 701, 757, 797, 809, 829, 857, 881, 937, 953, 997, 1013, 1049, 1069, 1093, 1109, 1117
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OFFSET

1,1


COMMENTS

First differences are multiples of 4 (which follows from set of differences of the moduli in the Noe formula). Minimal difference 4 occurs at a(1)=17, a(25)=673, a(48)=1297, etc.  Zak Seidov, Oct 04 2014


REFERENCES

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


LINKS



FORMULA

Same as primes congruent to {1, 9, 13, 17, 25, 29, or 49} (mod 52).  T. D. Noe, Apr 29 2008 [See e.g. Cox, p. 36.  N. J. A. Sloane, May 27 2014]


MATHEMATICA

QuadPrimes2[1, 0, 13, 10000] (* see A106856 *)


PROG

(PARI) is_A033210(n)={vecsearch([1, 9, 13, 17, 25, 29, 49], n%52)&&isprime(n)} \\ setsearch() is still slower by a factor > 2.  M. F. Hasler, Oct 04 2014


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



STATUS

approved



