A068488 m for which p(m) is the least prime dividing #p(n) + 1, i.e., primorial n-th prime augmented by 1 (A005234).

2, 4, 11, 47, 344, 17, 8, 69, 66, 67, 8028643011, 42, 18, 39, 162, 21, 59, 48, 2311331257, 179, 369, 2477, 23289, 32, 172011, 75668, 342, 35, 28757, 356411, 243, 297, 152

Offset: 1

Author

Lekraj Beedassy, Mar 11 2002

Keywords

• nonn
• hard
• more

Comments

Since #P34 + 1 has two rather large factors, we need the number of primes less than or equal to 678279959005528882498681487.

Links

• R. Mestrovic, Euclid's theorem on the infinitude of primes: a historical survey of its proofs (300 BC--2012) and another new proof, arXiv preprint arXiv:1202.3670 [math.HO], 2012-2018. - From N. J. A. Sloane, Jun 13 2012
• Hisanori Mishima, Factorization results #Pn (Primorial) + 1

Crossrefs

Cf. A068489.

Programs

Mathematica

Do[ Print[ PrimePi[ FactorInteger[ Product[ Prime[k], {k, 1, n}] + 1] [[1, 1]]]], {n, 1, 20} ]

Formula

a(n) = PrimePi(A051342).

Extensions

Edited and extended by Robert G. Wilson v, Mar 12 2002