A066268 Product of first n primorials - 1.

1, 11, 359, 75599, 174635999, 5244319079999, 2677277333530799999, 25968760179275365451999999, 5793445238736255798985527239999999, 37481813439427687898244906452608585199999999, 7517370874372838151564668004911177464757864075999999999

Offset: 1

Author

Patrick De Geest, Dec 16 2001

Keywords

• nonn

Examples

			a(3) = (2)*(2*3)*(2*3*5) - 1 = 359.
		

Links

• Harry J. Smith, Table of n, a(n) for n = 1..37
• Romeo Meštrović, 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], 2012-2023. - From N. J. A. Sloane, Jun 13 2012
• Carlos Rivera, Puzzle 118. Primorial product numbers, The Prime Puzzles & Problems Connection.
• Eric Weisstein's World of Mathematics, Primorial.

Crossrefs

Cf. A066266, A066267, A066269, A002110, A006939, A006794.

Programs

Mathematica

Table[Times@@Table[Times@@Prime[Range[n]],{n,k}]-1,{k,40}]
(* or *)
pr2=1; Table[pr1=1; Do[pr1=pr1*Prime[n],{n,k}]; pr2=pr2*pr1; pr2-1,{k,40}] (* Jayanta Basu, May 12 2013 *)

PARI

a(n) = -1 + prod(k=1, n, prime(k)^(n-k+1)) \\ Andrew Howroyd, Dec 10 2024

Formula

a(n) = A006939(n) - 1. - Andrew Howroyd, Dec 10 2024

Extensions

Offset changed from 0 to 1 by Harry J. Smith, Feb 08 2010