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A139854 Primes of the form 3x^2 + 40y^2. 3
3, 43, 67, 163, 283, 307, 523, 547, 643, 787, 883, 907, 1123, 1483, 1627, 1723, 1747, 1867, 1987, 2083, 2203, 2347, 2467, 2683, 2707, 2803, 3067, 3163, 3187, 3307, 3547, 3643, 3907, 4003, 4027, 4243, 4363, 4483, 4507, 4603, 4723, 4987, 5107 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Discriminant=-480. See A139827 for more information.

Except for 3, also primes of the form 27x^2+12xy+28y^2. See A140633. - T. D. Noe, May 19 2008

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)

FORMULA

Except for 3, the primes are congruent to {43, 67} (mod 120).

MATHEMATICA

QuadPrimes2[3, 0, 40, 10000] (* see A106856 *)

PROG

(Magma) [3] cat [ p: p in PrimesUpTo(6000) | p mod 120 in {43, 67}]; // Vincenzo Librandi, Jul 29 2012

(PARI) list(lim)=my(v=List(), w, t); for(x=1, sqrtint(lim\3), w=3*x^2; for(y=0, sqrtint((lim-w)\40), if(isprime(t=w+40*y^2), listput(v, t)))); Set(v) \\ Charles R Greathouse IV, Feb 22 2017

CROSSREFS

Cf. A140633.

Sequence in context: A253577 A337213 A059802 * A194578 A185632 A006033

Adjacent sequences: A139851 A139852 A139853 * A139855 A139856 A139857

KEYWORD

nonn,easy

AUTHOR

T. D. Noe, May 02 2008

STATUS

approved

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Last modified November 29 18:13 EST 2022. Contains 358431 sequences. (Running on oeis4.)