Mersenne Twister

A good general purpose PseudoRandomNumberGenerator.

This is the basic PRNG for PythonLanguage and RubyLanguage, and it or one like it (i.e. fast and with a large period) should be adopted by every language under the sun.

It is annoying that PythonLanguage and many other implementations, including PerlLanguage, only allow one LongInteger? as a seed, even though there are 624 unsigned longs (2496 bits) holding the state of the generator, and the CeeLanguage reference implementation does allow a full seed.

But in Python the LongInteger? can be arbitrarily long... So where's the problem (for Python)?

See http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/emt.html.

See IndirectionShiftAccumulateAddCount for a fast big PRNG that's cryptographically strong.