%I #33 Jan 15 2024 09:36:58

%S 3,13,361,75601,174636001,5244319080001,2677277333530800001,

%T 25968760179275365452000001,5793445238736255798985527240000001,

%U 37481813439427687898244906452608585200000001

%N Product of first n primorials + 1.

%H Harry J. Smith, <a href="/A066266/b066266.txt">Table of n, a(n) for n = 1..37</a>

%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 Carlos Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_118.htm">Puzzle 118. Primorial product numbers</a>, The Prime Puzzles & Problems Connection.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Primorial.html">Primorial.</a>

%e a(3)=361 since 361 = (2)*(2*3)*(2*3*5) + 1.

%t Table[Times@@Table[Times@@Prime[Range[n]],{n,k}]+1,{k,40}] (* _Jayanta Basu_, May 12 2013 *)

%t Rest[FoldList[Times,1,Rest[FoldList[Times,1,Prime[Range[10]]]]]]+1 (* _Harvey P. Dale_, Sep 16 2013 *)

%o (PARI) { p=1; q=1; for (n=1, 37, p*=prime(n); q*=p; write("b066266.txt", n, " ", q + 1) ) } \\ _Harry J. Smith_, Feb 08 2010

%Y Cf. A066267, A066268, A066269, A002110, A006939, A005234.

%K nonn

%O 1,1

%A _Patrick De Geest_, Dec 16 2001

%E Offset changed from 0 to 1 by _Harry J. Smith_, Feb 08 2010