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infinite_prime_sq_add_one

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Are there infinitely many primes $p$ such that $p - 1$ is a perfect square? In other words: Are there infinitely many primes of the form $n^2 + 1$?

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Lean 4 Statement 
theorem infinite_prime_sq_add_one :
    answer(sorry) ↔ {n : ℕ | Prime (n^2 + 1)}.Infinite
ID: Wikipedia__PrimesAndPerfectSquares__infinite_prime_sq_add_one
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