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%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
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