25528Brun's constant in a different context
- Apr 2 5:57 PMhi
so I've been trying for awhile to write an asymptotic formula for
sum p_n<=x 1/(p_n - p(n-1))
(the sum of reciprocals of prime gaps)
where p_n means nth prime and n>1.
my attempt is this
where A=approx 0.37787 and B is Brun's constant.
The value of A is ln(2*C_twin)+1/10, and the error term is very small even for large x. Can someone verify this please? I can send you a spreadsheet if you like, I've tested this up to 500,000..
thanks from Guy
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