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2019-07-19, 05:33   #3
CRGreathouse

Aug 2006

3×1,973 Posts

Quote:
 Originally Posted by Dylan14 And secondly, per Tomas Oliveira e Silva, the number of twin primes have been calculated to at least 4*10^18 (about exp(42.833)). You want a twin prime count near exp(88), which is about 1.65*10^38. Yeah, I don’t foresee a calculation of that being feasible anytime soon.
As a ballpark figure, Oliveira e Silva's calculation probably took in the neighborhood of $10,000 to$100,000 of compute time. Counting twin primes scales, at best, as x/log log x (practically speaking, it's superlinear) so ~ 3e23 dollars or ~ 4 billion years worth of gross world product. Knock off a couple of zeros for efficiency improvements and a few more for as many generations of Moore's law as you're willing to count on.