A369105 Primes p such that p+2 has only prime factors congruent to -1 modulo 4.

5, 7, 17, 19, 29, 31, 41, 47, 61, 67, 79, 97, 101, 127, 131, 137, 139, 149, 197, 199, 211, 229, 241, 251, 269, 277, 281, 307, 359, 379, 397, 421, 439, 461, 467, 487, 499, 521, 569, 571, 587, 601, 617, 619, 631, 641, 647, 691, 709, 719, 727, 751, 757, 787, 809, 811

Offset: 1

Author

Stefano Spezia, Jan 13 2024

Keywords

• nonn

Comments

Jones and Zvonkin call these primes BCC primes, where BCC stands for Bujalance, Cirre, and Conder.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• E. Bujalance, F. J. Cirre, and M. D. E. Conder, Bounds on the orders of groups of automorphisms of a pseudo-real surface of given genus, Journal of the London Mathematical Society, Volume 101, Issue 2, p. 877-906, (2019).
• Gareth A. Jones and Alexander K. Zvonkin, A number-theoretic problem concerning pseudo-real Riemann surfaces, arXiv:2401.00270 [math.NT], 2023. See page 1.

Crossrefs

Cf. A001221, A004614, A004767, A027748, A369107, A369108, A369109, A369111.

Programs

Mathematica

Select[Prime[Range[150]], PrimeQ[f=First/@FactorInteger[#+2]] == Table[True,{j,PrimeNu[#+2]}] && Mod[f,4] == Table[3, {m,PrimeNu[#+2]}] &]

PARI

is1(n) = {my(p = factor(n)[, 1]); for(i = 1, #p, if(p[i] % 4 == 1, return(0))); 1;};
lista(pmax) = forprime(p = 3, pmax, if(is1(p+2), print1(p, ", "))); \\ Amiram Eldar, Jun 03 2024