A249798 Numbers k such that the product of the first k primes minus the (k+1)-th prime is prime.

3, 4, 5, 6, 8, 22, 23, 24, 35, 73, 83, 147, 553, 1098, 1115, 1542, 2097, 2149, 8712, 19965, 25046, 30987, 38635

Offset: 1

Author

Ivan N. Ianakiev, Nov 06 2014

Keywords

• nonn
• more

Examples

			p(1)*p(2)*p(3)*p(4) - p(5) = 2*3*5*7 - 11 = 199. 199 is prime, therefore 4 is in the sequence.
		

Crossrefs

Cf. A000040, A093078.

Programs

Mathematica

Select[Range[1000],PrimeQ[Times@@(Prime[Range[#]])-Prime[#+1]]&]

PARI

lista(nn) = {prp = 1; for(n=1, nn, prp *= prime(n); if (isprime(prp-prime(n+1)), print1(n, ", ")););} \\ Michel Marcus, Nov 06 2014

Formula

a(n) = primepi(A093078(n)). - Michel Marcus, Nov 06 2014

Extensions

a(17)-a(18) using A093078 from Michael S. Branicky, Mar 18 2024

a(19)-a(23) from Henri Lifchitz, Nov 08 2024