A390918 Primes p such that the difference of the product of 4 consecutive primes starting with p and the sum of those 4 primes is a prime.

2, 3, 5, 17, 19, 41, 47, 79, 89, 127, 167, 227, 257, 337, 379, 397, 463, 557, 563, 631, 647, 701, 827, 877, 881, 937, 1201, 1217, 1279, 1399, 1487, 1549, 1567, 1571, 1609, 1721, 1811, 2027, 2297, 2459, 2657, 2741, 2753, 2909, 3137, 3181, 3329, 3371, 3389, 3449, 3527, 3769, 3797, 3851, 3917, 4261

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Formula

a(n) = prime(A390917(n)).

Example

a(4) = 17 is a term because the four consecutive primes starting with 17 are 17, 19, 23 and 29, and 17 * 19 * 23 * 29 - (17 + 19 + 23 + 29) = 215353 is prime.

Maple

map(ithprime, select(proc(t) local j;  isprime(mul(ithprime(j), j=t..t+3) - add(ithprime(j), j=t..t+3)) end proc, [$1..1000]));

Mathematica

Select[Partition[Prime[Range[1000]], 4, 1], PrimeQ[Times @@ # - Plus @@ #] &][[All, 1]] (* Paolo Xausa, Dec 01 2025 *)

Crossrefs

Cf. A390916, A390917, A390930. Contains A390929.

Sequence in context: A058501 A215356 A249410 * A119405 A032733 A111632

Adjacent sequences: A390915 A390916 A390917 * A390919 A390920 A390921

Keyword

nonn

Author

Will Gosnell and Robert Israel, Nov 23 2025

Status

approved