I known that it is not known whether there are infinitely many prime numbers of the form $2^n+1$ or not, but is there any heuristic approach to its asymptotic behavior?
Thank you.
2026-04-02 13:27:45.1775136465
What is the asymptotic behavior of the number of primes of the form $2^n+1$ lower than a given N?
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Once I read this beatiful article of Caldwell, explaining basic heuristic related to this kind of open problems. I think it is what you are searching (in particular, see Conjecture 1.2).