A349985 Primes of the form (product of 4 consecutive primes) + (sum of the same 4 consecutive primes).

227, 1181, 765169, 575772529, 1844619589, 7916858557, 31095441001, 37809636673, 75033373321, 80635078873, 234564891361, 302257557157, 443314943881, 463236781489, 1215371749321, 1347613229509, 1534404944209, 2967342092629, 5573043569437, 6390859845289

Offset

1,1

Comments

It is conjectured that this sequence is infinite, and that similar lists of primes can be generated by using any even number of consecutive primes. Specifying 2 consecutive primes results in A096342. However, it should be noted that the percentage of resulting primes (as compared to all numbers generated in this manner) decreases as the number of consecutive primes to consider increases.

Links

Lyle Blosser, Table of n, a(n) for n = 1..498

Example

227 is a term since 227 is prime and is generated by (2*3*5*7) + (2+3+5+7).
1181 is a term since 1181 is prime and is generated by (3*5*7*11) + (3+5+7+11).

Mathematica

Select[Table[s=NextPrime[p, Range@4-1]; Total@s+Times@@s, {p, Prime@Range@300}], PrimeQ] (* Giorgos Kalogeropoulos, Jan 09 2022 *)

Crossrefs

Cf. A096342.

Sequence in context: A176012 A031693 A158228 * A209843 A115998 A092324

Adjacent sequences: A349982 A349983 A349984 * A349986 A349987 A349988

Keyword

nonn

Author

Lyle Blosser, Jan 08 2022

Status

approved