Editing Fermat number (section)

==Applications of Fermat numbers==
===Pseudorandom number generation===
Fermat primes are particularly useful in generating pseudo-random sequences of numbers in the range 1, ..., ''N'', where ''N'' is a power of 2. The most common method used is to take any seed value between 1 and {{nowrap|''P'' − 1}}, where ''P'' is a Fermat prime. Now multiply this by a number ''A'', which is greater than the [[square root]] of ''P'' and is a [[Primitive root modulo n|primitive root]] modulo ''P'' (i.e., it is not a [[quadratic residue]]). Then take the result modulo ''P''. The result is the new value for the RNG.
: <math>V_{j+1} = (A \times V_j) \bmod P</math> (see [[linear congruential generator]])
This is useful in computer science, since most data structures have members with 2<sup>''X''</sup> possible values. For example, a byte has 256 (2<sup>8</sup>) possible values (0–255). Therefore, to fill a byte or bytes with random values, a random number generator that produces values 1–256 can be used, the byte taking the output value −1. Very large Fermat primes are of particular interest in data encryption for this reason. This method produces only [[pseudorandom]] values, as after {{nowrap|''P'' − 1}} repetitions, the sequence repeats. A poorly chosen multiplier can result in the sequence repeating sooner than {{nowrap|''P'' − 1}}.