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%I #33 Jan 15 2024 09:35:47
%S 1,11,359,75599,174635999,5244319079999,2677277333530799999,
%T 25968760179275365451999999,5793445238736255798985527239999999,
%U 37481813439427687898244906452608585199999999
%N Product of first n primorials - 1.
%H Harry J. Smith, <a href="/A066268/b066268.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) = (2)*(2*3)*(2*3*5) - 1 = 359.
%t Table[Times@@Table[Times@@Prime[Range[n]],{n,k}]-1,{k,40}]
%t (* or *)
%t pr2=1; Table[pr1=1; Do[pr1=pr1*Prime[n],{n,k}]; pr2=pr2*pr1; pr2-1,{k,40}] (* _Jayanta Basu_, May 12 2013 *)
%o (PARI) { p=1; q=1; for (n=1, 37, p*=prime(n); q*=p; write("b066268.txt", n, " ", q - 1) ) } \\ _Harry J. Smith_, Feb 08 2010
%Y Cf. A066266, A066267, A066269, A002110, A006939, A006794.
%K nonn
%O 1,2
%A _Patrick De Geest_, Dec 16 2001
%E Offset changed from 0 to 1 by _Harry J. Smith_, Feb 08 2010
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