A102273 Primes p such that Q(sqrt(-21p)) has genus characters chi_{-3} = -1, chi_{-7} = +1.

11, 23, 71, 107, 179, 191, 239, 263, 347, 359, 431, 443, 491, 599, 659, 683, 743, 827, 863, 911, 947, 1019, 1031, 1103, 1163, 1187, 1283, 1367, 1439, 1451, 1499, 1523, 1583, 1607, 1619, 1667, 1787, 1871, 2003, 2027, 2039, 2087

Offset: 1

Author

N. J. A. Sloane, Feb 19 2005

Keywords

• nonn

Comments

The 2-class number of these fields is always 4.

Primes of the form 2x^2 - 2xy + 11y^2 with x nonnegative and y positive. - T. D. Noe, May 08 2005

Also primes of the forms 8x^2 + 4xy + 11y^2 and 11x^2 + 2xy + 23y^2. See A140633. - T. D. Noe, May 19 2008

The discriminant of positive definite binary quadratic form (2,2,11) is -84. - Hugo Pfoertner, Jul 14 2019

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• H. Cohn and J. C. Lagarias, On the existence of fields governing the 2-invariants of the classgroup of Q(sqrt{dp}) as p varies, Math. Comp. 41 (1983), 711-730.
• N. J. A. Sloane et al., Binary Quadratic Forms and OEIS (Index to related sequences, programs, references)

Crossrefs

Cf. A102269-A102275.

Cf. A139827.

Programs

Magma

[p: p in PrimesUpTo(3000) | p mod 84 in [2, 11, 23, 71]]; // Vincenzo Librandi, Jul 19 2012

Mathematica

f[x_,y_]:=2*x^2+2*x*y+11*y^2; lst={};Do[Do[p=f[x,y];If[PrimeQ[p],AppendTo[lst,p]],{y,-5!,6!}],{x,-5!,6!}];Take[Union[lst],5! ] (* Vladimir Joseph Stephan Orlovsky, Jul 06 2009 *)

Formula

The primes are congruent to {2, 11, 23, 71} (mod 84). - T. D. Noe, May 02 2008