Quote:
Originally Posted by hal1se
if we wonder: twin system how like randomize, how different randomize?
please take two randomize integer in this range:
int(exp(44))44^8 to int(exp(44))+44^8.
and look: two integer, same time primes than count=count+1
44^8 times loop please.
question: count=~?
answer: count * 2,64 =~ twin prime count.

Assuming I understand you correctly, I created a Mathematica notebook to test this out (see attachment). However, due to timing constraints (I came to an estimate of 9.7 years to run the entire program), I ran the loop for 100 million iterations and then extrapolated to get the twin count. I then compared that to primesieve 7.4 and the number I got was less than 1% off the primesieve value. So in this case your idea makes sense. Some questions I have though:
1. Does this work for larger n than 44?
2. Continuing on this question, what is the asymptotic behavior of doing this if we replace 44 with n and let n go to infinity? Do we get the actual twin prime count, or does it diverge (and if so, does it grow or shrink relative to the actual value)?