A103783 Primes of the form primorial P(k)*n-1 with minimal n, n>0, k>=2.

5, 29, 419, 2309, 30029, 1021019, 19399379, 669278609, 38818159379, 601681470389, 14841476269619, 304250263527209, 235489703970060539, 1844669347765474229, 228124109340330313109, 24995884552004764307909

Offset: 1

Author

Lei Zhou, Feb 15 2005

Keywords

• nonn

Comments

Weak conjecture: sequence is defined for all k>=2; strong conjecture: n<(prime(k))^2;

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

Examples

			P(2)*1-1=5 is prime, so a(2)=5;
P(9)*3-1=669278609 is prime, so a(9)=669278609;
		

Crossrefs

Cf. A002110, A103515, A103782, A073917, A214089.

Programs

Mathematica

nmax = 2^2048; npd = 2; n = 2; npd = npd*Prime[n]; While[npd < nmax, tt = 1; cp = npd*tt - 1; While[(tt <= (Prime[n])^2) && (! (PrimeQ[cp])), tt = tt + 1; cp = npd*tt - 1]; Print[cp]; n = n + 1; npd = npd*Prime[n]]