A035345 Smallest prime > prime(1)*prime(2)*...*prime(n)+1.

3, 5, 11, 37, 223, 2333, 30047, 510529, 9699713, 223092907, 6469693291, 200560490197, 7420738134871, 304250263527281, 13082761331670077, 614889782588491517, 32589158477190044789, 1922760350154212639131

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Examples

			Next prime after 2*3*5 + 1 = 31 is 37, so a(3)=37.
		

Links

• S. W. Golomb, The evidence for Fortune's conjecture, Math. Mag. 54 (1981), 209-210.
• Eric Weisstein's World of Mathematics, Fortunate Prime

Crossrefs

Cf. A002110, A005235, A006862, A038710.

Programs

Mathematica

Table[NextPrime[Product[Prime@ k, {k, n}] + 1], {n, 0, 17}] (* Michael De Vlieger, Dec 02 2015 *)

PARI

a(n) = nextprime(2+factorback(primes(n))); \\ Michel Marcus, Dec 24 2022

Python

from sympy import nextprime, primorial
def a(n): return nextprime(1 + (primorial(n) if n else 1))
print([a(n) for n in range(18)]) # Michael S. Branicky, Dec 24 2022

Formula

a(n) = A002110(n) + A005235(n) for n > 0. - Jonathan Sondow, Dec 02 2015