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
Famous quotes containing the word large:
“The old, subjective, stagnant, indolent and wretched life for woman has gone. She has as many resources as men, as many activities beckon her on. As large possibilities swell and inspire her heart.”
—Anna Julia Cooper (1859–1964)