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 human mind is capable of excitement without the application of gross and violent stimulants; and he must have a very faint perception of its beauty and dignity who does not know this.”
—William Wordsworth (1770–1850)
“My tendency to nervousness in my younger days, in view of the fact of a number of near relatives on both my father’s and mother’s side of the house having become insane, gave some serious uneasiness. I made up my mind to overcome it.... In the cross-examination of witnesses before a crowded court-house ... I soon found I could control myself even in the worst of testing cases. Finally, in battle.”
—Rutherford Birchard Hayes (1822–1893)
“Counting is the religion of this generation it is its hope and its salvation.”
—Gertrude Stein (1874–1946)