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Instead of using probabilistic methods to generate large primes, as indicated in the other answers, one can (IMHO better) employ Maurer's algorithm of generating provable primes. I have a Python code implementing that algorithm, available at


What you could do, is use a Mill's constant for generation. Then, a test for primarity would be good anyways...(in case that not exact enough constant is chosen, so you could end up with non prime) Mill's constant is such a number, that if powered to 3, and then powered to any N, where N is an usigned integer, we get value V wich, rounded down, is a prime. ...

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