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Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions

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Time estimate to determine if a number is prime [closed]

How long does it take to verify that a given number is a prime number, as a function of its number of digits, in a personal computer, say? How computationally hard is this?
Marco M.'s user avatar