A107180 Primes of the form 2x^2 + 35y^2.
2, 37, 43, 53, 67, 107, 163, 197, 277, 317, 347, 373, 443, 547, 557, 613, 653, 683, 757, 827, 877, 883, 907, 947, 1093, 1117, 1163, 1187, 1213, 1283, 1373, 1453, 1493, 1523, 1597, 1667, 1723, 1733, 1747, 1787, 1877, 1933, 1997, 2003, 2027, 2053
Offset: 1
Links
- Vincenzo Librandi and Ray Chandler, Table of n, a(n) for n = 1..10000 [First 1000 terms from Vincenzo Librandi]
- N. J. A. Sloane et al., Binary Quadratic Forms and OEIS (Index to related sequences, programs, references)
Crossrefs
Cf. A139827.
Programs
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Magma
[ p: p in PrimesUpTo(3000) | p mod 280 in {2, 37, 43, 53, 67, 93, 107, 123, 163, 197, 253, 267, 277} ]; // Vincenzo Librandi, Jul 26 2012 -
Mathematica
QuadPrimes2[2, 0, 35, 10000] (* see A106856 *)
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PARI
list(lim)=my(v=List(),w,t); for(x=1, sqrtint(lim\2), w=2*x^2; for(y=0, sqrtint((lim-w)\35), if(isprime(t=w+35*y^2), listput(v,t)))); Set(v) \\ Charles R Greathouse IV, Feb 10 2017
Formula
The primes are congruent to {2, 37, 43, 53, 67, 93, 107, 123, 163, 197, 253, 267, 277} (mod 280). - T. D. Noe, May 02 2008
Comments