What is the fraction of primes that are twin primes up to ten million?

[Ackbach]

Here is this week's POTW:

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Twin primes are primes that differ by 2. Find the fraction of the primes up to ten million that are twin primes. For example, 3 and 5 are twin primes, as well as 5 and 7, and all the primes less than 10 are 2, 3, 5, and 7. Hence the fraction of twin primes in the interval [1,10] is 3/4.

Does your answer give you any sort of hunch about the number of twin primes? (The Twin Primes Conjecture is one of the great unsolved problems in Number Theory.)

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[Ackbach]

No one answered this week's POTW. Here is my solution, written in the Wolfram Language:

Spoiler

View attachment 5303