MersenneTwister

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)?

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

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