PRNGs which are not CSPRNG From Definition of CSPRNG, it has two characteristics


It satisfies the next-bit test.
It withstands 'state compromise extensions' - part of all of the state being compromised does not allow for reconstruction of the prior stream of random numbers.


I am looking for PRNGs which fail the 2nd Characteristic. Infact they are PRNG but not CSPRNG.
Item (2) is not part of the definition of a standard CSPRNG. If you look at where this definition was taken from in Wikipedia, this item refers to a "forward secure CSPRNG". So, this is a definition of forward security and not the standard notion.

Also, the next-bit test is one way of defining, but certainly not the only way.

In any case, it is easy to construct a CSPRNG that is not forward secure; simply always store the initial state.