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:
“I think that a young state, like a young virgin, should modestly stay at home, and wait the application of suitors for an alliance with her; and not run about offering her amity to all the world; and hazarding their refusal.... Our virgin is a jolly one; and tho at present not very rich, will in time be a great fortune, and where she has a favorable predisposition, it seems to me well worth cultivating.”
—Benjamin Franklin (1706–1790)
“Cultivated labor drives out brute labor. An infinite number of shrewd men, in infinite years, have arrived at certain best and shortest ways of doing, and this accumulated skill in arts, cultures, harvestings, curings, manufactures, navigations, exchanges, constitutes the worth of our world to-day.”
—Ralph Waldo Emerson (1803–1882)
“Our Indian said that he was a doctor, and could tell me some medicinal use for every plant I could show him ... proving himself as good as his word. According to his account, he had acquired such knowledge in his youth from a wise old Indian with whom he associated, and he lamented that the present generation of Indians “had lost a great deal.””
—Henry David Thoreau (1817–1862)