A356727 Primes of the form 4*k^2 + 84*k + 43.

43, 131, 227, 331, 443, 563, 691, 827, 971, 1123, 1283, 1451, 1627, 1811, 2003, 2203, 2411, 2851, 3083, 3323, 3571, 4091, 4363, 4643, 4931, 5227, 5531, 5843, 6163, 6491, 6827, 7523, 7883, 8627, 9011, 9403, 9803, 10211, 10627, 11483, 11923, 13291, 13763, 14243, 14731, 15227, 15731

Offset: 1

Author

Charles Delaporte, Aug 24 2022

Keywords

• nonn
• less

Comments

The polynomial 4*k^2 + 84*k + 43 has prime values for k from 0 to 16. The proportion of prime numbers (23.28%) obtained among the first ten million values is slightly higher than that (22.08%) obtained with Euler's polynomial k^2 - k + 41.

The polynomial 4*k^2 + 84*k + 43 produces a Hardy-Littlewood constant of 7.3291180993696....

Links

• Eric Weisstein's World of Mathematics, Prime generating polynomial

Crossrefs

Cf. A005846, A221712, A331940.

Programs

Mathematica

Select[Table[4k^2+84k+43,{k,0,60}],PrimeQ] (* Harvey P. Dale, May 07 2023 *)