%I #8 Jul 03 2012 16:01:28

%S 5,29,419,2309,30029,1021019,19399379,669278609,38818159379,

%T 601681470389,14841476269619,304250263527209,235489703970060539,

%U 1844669347765474229,228124109340330313109,24995884552004764307909

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

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

%C Smallest prime p such that the prime factorization of p+1 contains the first n+1 primes. - _R. J. Mathar_, Jul 03 2012

%e P(2)*1-1=5 is prime, so a(2)=5;

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

%t 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]]

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

%K nonn

%O 1,1

%A _Lei Zhou_, Feb 15 2005