Large Primes
For the large primes used in cryptography, it is usual to use a modified form of sieving: a randomly-chosen range of odd numbers of the desired size is sieved against a number of relatively small odd primes (typically all primes less than 65,000). The remaining candidate primes are tested in random order with a standard primality test such as the Miller-Rabin primality test for probable primes.
Alternatively, a number of techniques exist for efficiently generating provable primes. These include generating prime numbers p for which the prime factorization of p − 1 or p + 1 is known.
Read more about this topic: Generating Primes
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“For a large class of cases—though not for all—in which we employ the word “meaning” it can be defined thus: the meaning of a word is its use in the language.”
—Ludwig Wittgenstein (1889–1951)