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:
“Great abilites are not requisite for an Historian; for in historical composition, all the greatest powers of the human mind are quiescent. He has facts ready to his hand; so there is no exercise of invention. Imagination is not required in any degree; only about as much as is used in the lowest kinds of poetry. Some penetration, accuracy, and colouring, will fit a man for the task, if he can give the application which is necessary.”
—Samuel Johnson (1709–1784)
“To make life more bearable and pleasant for everybody, choose the issues that are significant enough to fight over, and ignore or use distraction for those you can let slide that day. Picking your battles will eliminate a number of conflicts, and yet will still leave you feeling in control.”
—Lawrence Balter (20th century)
“This generation has come into the world fatally late for some enterprises. Go where we will on the surface of things, men have been there before us.... But the lives of men, though more extended laterally in their range, are still as shallow as ever.”
—Henry David Thoreau (1817–1862)