%I #28 Jan 15 2024 10:03:13

%S 3,10,5,343,3248,18,16,12,22,20324,50,9414916809095,13120,43,8481,

%T 1200361259,196,38,10326732314,65,38,34

%N m for which prime(m) is the least prime dividing #prime(n) - 1, i.e., one less than primorial n-th prime (A057588).

%C Since #P13 - 1 is a prime, see A006794, we need the number of primes less than or equal to #P13 - 1. The sequence continues, for n=14 to 23: 13120, 43, 8481, 1200361259, 196, 38, 10326732314, 65, 38, 34.

%C a(24) = pi(23768741896345550770650537601358309). - _Donovan Johnson_, Dec 08 2009

%H Romeo Meštrović, <a href="http://arxiv.org/abs/1202.3670">Euclid's theorem on the infinitude of primes: a historical survey of its proofs (300 BC--2012) and another new proof</a>, arXiv preprint arXiv:1202.3670 [math.HO], 2012-2023. - From N. J. A. Sloane, Jun 13 2012

%H Hisanori Mishima, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/mathland/matha1/matha103.htm">Factorization results #Pn (Primorial) - 1</a>.

%F a(n) = A000720(A057713(n)).

%t Do[ Print[ PrimePi[ FactorInteger[ Product[ Prime[k], {k, 1, n}] - 1] [[1, 1]]]], {n, 2, 22} ]

%Y Cf. A000720, A006794, A057588, A057713, A068488.

%K hard,more,nonn

%O 2,1

%A _Lekraj Beedassy_, Mar 11 2002

%E Edited and extended by _Robert G. Wilson v_, Mar 12 2002

%E a(13) from _Donovan Johnson_, Dec 08 2009