Application in (pseudo-)random Number Generation
Sophie Germain primes have a practical application in the generation of pseudo-random numbers. The decimal expansion of 1/q will produce a stream of q − 1 pseudo-random digits, if q is the safe prime of a Sophie Germain prime p, with p congruent to 3, 9, or 11 (mod 20). Thus “suitable” prime numbers q are 7, 23, 47, 59, 167, 179, etc. (corresponding to p = 3, 11, 23, 29, 83, 89, etc.). The result is a stream of length q − 1 digits (including leading zeros). So, for example, using q = 23 generates the pseudo-random digits 0, 4, 3, 4, 7, 8, 2, 6, 0, 8, 6, 9, 5, 6, 5, 2, 1, 7, 3, 9, 1, 3. Note that these digits are not appropriate for cryptographic purposes, as the value of each can be derived from its predecessor in the digit-stream.
Read more about this topic: Sophie Germain Prime
Famous quotes containing the words application, number and/or generation:
“The receipt to make a speaker, and an applauded one too, is short and easy.—Take of common sense quantum sufficit, add a little application to the rules and orders of the House, throw obvious thoughts in a new light, and make up the whole with a large quantity of purity, correctness, and elegancy of style.”
—Philip Dormer Stanhope, 4th Earl Chesterfield (1694–1773)
“The genius of democracies is seen not only in the great number of new words introduced but even more in the new ideas they express.”
—Alexis de Tocqueville (1805–1859)
“One generation abandons the enterprises of another like stranded vessels.”
—Henry David Thoreau (1817–1862)