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

Author

Lyle Blosser, Jan 08 2022

Keywords

• nonn

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.

Examples

			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).
		

Links

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

Crossrefs

Cf. A096342.

Programs

Mathematica

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