Looking at the PCG paper, it shows that a basic XorShift generator doesn't pass statistical tests as it gets bigger. Basically, there are some tests it never p

Looking at the PCG paper, it shows that a basic XorShift generator doesn't pass statistical tests as it gets bigger. Basically, there are some tests it never passes no matter how big it gets. But a tiny change (XorShift*) is enough to get a generator that passes empirical statistical tests. The page about other RNGs has lots of good info about this stuff.