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Answers suggest hat you basically pick a random large odd number, and add 2 to it until your selected primality test passes.
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The prime number theorem tells us that the probability that a number between 1 and is a prime number is .
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Therefore, for an N-bit integer, we only have to run the test N times on average to find a prime.
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Since say, A 512-bit integer is already humongous and sufficiently large, we would only need to search 512 times on average even for such sizes, and therefore the procedure scales well.
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