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Decimal expansion of Sum_{n>0} Product_{m=1..n} 1/(Prime(m+1)-Prime(m)).
1

%I #6 Jul 28 2015 00:01:27

%S 1,8,5,6,7,0,8,6,1,6,2,9,0,1,3,6,0,9,9,0,8,3,9,6,6,7,8,9,5,1,2,4,5,2,

%T 2,5,1,3,8,4,6,0,3,2,7,7,1,6,1,1,9,5,9,8,2,7,9,4,8,1,8,8,6,0,8,6,7,8,

%U 6,0,4,5,0,0,8,6,7,1,6,9,6,1,3,2,2,1,9,0,7,4,6,2,7,2,8,3,4,7,1,2,5,6,5,4,9

%N Decimal expansion of Sum_{n>0} Product_{m=1..n} 1/(Prime(m+1)-Prime(m)).

%e 1.85670861629013609908396678951245225138460327716119598279481886086...

%t RealDigits[ Sum[ Product[1/(Prime[m + 1] - Prime[m]), {m, n}], {n, 160}], 10, 111][[1]] (* _Robert G. Wilson v_, Nov 09 2004 *)

%K nonn,cons

%O 1,2

%A _Roger L. Bagula_, Nov 06 2004

%E Edited by _Robert G. Wilson v_, Nov 09 2004