Properties of PRNG / Hashes?
Mersenne Twister (as an example) is a fast random number generator, and has good properties (long period, good distribution) for most applications of random numbers (like statistics, simulations, modelling).

For cryptographic applications, we need more: We need a cryptographically secure random number generator. Such a function (implemented by an algorithm) has the property that an attacker has no means of to distinguishing the output from a pure random bit sequence, if he does not know the seed.

Such CSPRNGs (cryptographically secure random number generators) can be build from several other cryptographic primitives:


cryptographic hash functions
block ciphers
stream ciphers


All these primitives effectively need the properties of a "normal" PRNG, thus they are usable as such.

On the other hand, the algorithms implementing such primitives are normally a lot slower than "normal" PRNG - thus don't use iterated SHA-1 when Mersenne Twister is enough for your needs.