A073917 Smallest prime which leaves a remainder 1 when divided by primorial(n), i.e., when divided by first n primes.

3, 7, 31, 211, 2311, 120121, 4084081, 106696591, 892371481, 71166625531, 200560490131, 29682952539241, 2129751844690471, 78496567990020181, 8608456956238879741, 97767475431570134191, 9613801750771063195351

Offset: 1

Author

Amarnath Murthy, Aug 18 2002

Keywords

• nonn

Comments

Let Pr(n) = the product of first n primes. Then a(n) is the smallest prime of the form k*Pr(n) + 1. k = 1 for first five terms.

Smallest prime p such that the prime factorization of p-1 contains the first n primes. - R. J. Mathar, Jul 03 2012

Links

• T. D. Noe, Table of n, a(n) for n = 1..150

Crossrefs

Cf. A002110 (primorials), A073915, A103783, A214089.

Cf. A076689 (values of k).

Programs

PARI

a(n)=if(n<0,0,s=1; while(prime(s)%prod(i=1,n, prime(i))>1,s++); s)

Extensions

More terms from Vladeta Jovovic, Aug 20 2002