A382285 Initial members of prime octuplets (p, p+4, p+12, p+24, p+28, p+40, p+48, p+52), where all primes are consecutive primes.

241639, 44533249, 120833809, 245843149, 480454939, 547838359, 945331939, 1272712579, 1318911019, 1334157859, 1413122899, 1801178629, 1977960949, 2708995099, 3073533559, 3234255499, 3359304829, 3485412349, 3836960419, 4202567899, 4311168259, 4984840999, 5044981129

Offset: 1

Author

Federico Salas, Mar 20 2025

Keywords

• nonn

Comments

All gaps are twice the length of respective gaps in the prime octuplet form, (p, p+2, p+6, p+12, p+14, p+20, p+24, p+26). See A022012 for initial members of that pattern.

Terms are congruent to 19 (mod 30).

It is conjectured that there is an infinite number of primes for every admissible k-tuple.

Links

• Eric Weisstein's World of Mathematics, k-Tuple Conjecture.

Crossrefs

Cf. A022012.

Programs

PARI

list(lim) = {my(d0 = [4, 8, 12, 4, 12, 8, 4], s = vecsum(d0), d = vector(7, i, prime(i+1) - prime(i)), prv = 19); forprime(p = 23, lim, d = concat(vecextract(d, "^1"), p - prv); if(d == d0, print1(p - s, ", ")); prv = p);} \\ Amiram Eldar, Mar 21 2025

Extensions

More terms from Amiram Eldar, Mar 21 2025