A253941 Primes p such that (p^2 + 5)/6, (p^4 + 5)/6, (p^6 + 5)/6, (p^8 + 5)/6 and (p^10 + 5)/6 are all prime.

184279409, 619338131, 913749803, 1057351301, 1507289869, 1600204213, 2845213937, 4725908767, 4760956439, 5374709801, 5518707641, 8724256757, 9044067313, 9387396269, 10992352517, 11937043567, 13493126359, 13593105793, 17891702891, 17897035213, 17954907767, 19690938161, 20227580927, 20922685813, 21313027583, 21717176851

Offset

1,1

Comments

The sequence contains all terms up to 10^10. There are no terms as yet for which (p^12 + 5)/6 is also prime.

No terms < 10^11 with (p^12 + 5)/6 prime. - Chai Wah Wu, Jan 27 2015

Links

Chai Wah Wu, Table of n, a(n) for n = 1..67

Prog

(Python)
from gmpy2 import is_prime, t_divmod
A253941_list = []
for p in range(1, 10**6, 2):
    if is_prime(p):
        p2, x = p**2, 1
        for i in range(5):
            x *= p2
            q, r = t_divmod(x+5, 6)
            if r or not is_prime(q):
                break
        else:
            A253941_list.append(p) # Chai Wah Wu, Jan 22 2015
(PARI) lista(nn) = forprime(p=5, nn, if(ispseudoprime((p^2 + 5)/6) && ispseudoprime((p^4 + 5)/6) && ispseudoprime((p^6 + 5)/6) && ispseudoprime((p^8 + 5)/6) && ispseudoprime((p^10 + 5)/6), print1(p, ", "))); \\ Jinyuan Wang, Mar 01 2020

Crossrefs

Subsequence of A253976.

Cf. A118915, A247478, A253925, A253940.

Sequence in context: A226589 A201557 A234050 * A230222 A061440 A064593

Adjacent sequences: A253938 A253939 A253940 * A253942 A253943 A253944

Keyword

nonn

Author

Zak Seidov, Jan 20 2015

Extensions

a(15)-a(26) from Chai Wah Wu, Jan 22 2015

Status

approved