A389333 Primes p such that the sum and difference of the fourth power of the sum of 4 consecutive primes starting with p and the product of those primes are both prime.

7, 29, 1567, 2179, 2237, 4259, 5399, 12239, 14221, 14369, 21773, 26099, 28597, 41521, 44021, 47041, 48221, 48857, 49459, 56009, 58271, 63809, 64217, 65899, 83857, 86689, 93701, 94111, 98179, 102607, 110819, 117881, 133657, 136751, 151517, 153001, 154159, 166273, 167429, 169789, 180907, 182639

Offset

1,1

Comments

prime(k) where A034963(k)^4 + A046302(k) and A034963(k)^4 - A046302(k) are both prime.

Links

Robert Israel, Table of n, a(n) for n = 1..2000

Example

a(2) = 29 is a term because the four consecutive primes starting with 29 are 29, 31, 37, and 41, with sum 138 and product 1363783, and 138^4 - 1363783 = 361310153 and 138^4 + 1363783 = 364037719 are both prime.

Maple

P:= select(isprime, [2, seq(i, i=3..10^6, 2)]):
S4:= [seq(P[i]+P[i+1]+P[i+2]+P[i+3], i=1..nops(P)-3)]:
P4:= [seq(P[i]*P[i+1]*P[i+2]*P[i+3], i=1..nops(P)-3)]:
J:= select(i -> isprime(S4[i]^4 - P4[i]) and isprime(S4[i]^4 + P4[i]) , [$1..nops(P4)]):
P[J];

Crossrefs

Cf. A034963, A046302.

Sequence in context: A122119 A300528 A243623 * A157422 A061644 A053621

Adjacent sequences: A389330 A389331 A389332 * A389334 A389335 A389336

Keyword

nonn

Author

Will Gosnell and Robert Israel, Dec 14 2025

Status

approved