View Single Post 2019-08-04, 18:12   #7
Dylan14

"Dylan"
Mar 2017

3×173 Posts 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)?
Attached Files hallsetwinproblem.7z (362.0 KB, 47 views)  