Special types of prime numbers We know that there is infinitely many of prime by the proof of Euclidean.and we know also that there are infinitely many of primes in  arithmetic progression by the Dirichlet theorem
My question is, are there some special types of prime number that it has proven that there is infinitely many of them like the Fermat prime or the Sophie German prime or any other special types?


There are infinitely many primes that divide Fibonacci numbers.

See for instance

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*Infinite primes via Fibonacci numbers
and the original paper

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*Another proof of the infinite primes theorem
