[seqfan] more digits of sum over squared inverse twin primes

Richard Mathar mathar at strw.leidenuniv.nl
Sat May 30 19:10:30 CEST 2009

The current entry of  0.237251058
seems to be incorrect in at least three decimal digits.
I guess it is defined as the sum over all 1/A001359(n)^2+1/A006512(n)^2.
Gathering twin primes up to prime(1070000) the constant
is at least 0.23725177606 .
Someone with some spare computer cycles---not the cycles that spin the
computer and the earth around the sun in a year but the other, quicker ones---
might test whether the 0.23725177 may turn to 0.23725178 later on.

Richard Mathar
snapshots of results:
prime(900000)  0.23725177594...
prime(1290000) 0.23725177616...

Digits := 40 ;
x := 0.0 ;
for n from 1 do
        p := ithprime(n) ;
        if isprime(p+2) then
                x := evalf(x+1/p^2+1/(p+2)^2) ;
        if n mod 10000 = 0 then
        print(n,x) ;

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