A customer filed the following bug report on Connect:

While investigating the period of various random number generators, I found a serious bug in Microsoft .NET System.Random implementation.

Microsoft Documentation says that the Random class is based on Donald E. Knuth's subtractive random number generator algorithm. For more information, see D. E. Knuth. "The Art of Computer Programming, volume 2: Seminumerical Algorithms". Addison-Wesley, Reading, MA, second edition, 1981.

The problem was discovered when I use .NET Reflector to see what is actually implemented. Knuth was very specific about the lagged Fibonacci sequence coefficient (24 and 55). Somehow Microsoft mistyped the value to be 21 (this.inextp = 0x15 in public Random(int Seed) in source code), in place of 31 (=55-24). Due to this mistype, the random number generated no longer has the guanrantee on the period to be longer than (2^55-1). The Knuth version of lags (24, 55) has been tested by many people about the property of the generated numbers but not the one created by Microsoft.

It is very easy to identify the typo. It seems that Microsoft just copied the routine (ran3) from Numerical Recipes v.2 page. 283 verbatim (even the variable names are copied), not from Knuth book which has a complete different way of initializing. You see that Numerical Recipe version uses 31 correctly, not 21 used by Microsoft.

Looking at the sources, it seems it's still the case today.

I'm not sure what the implication of our deviation is. If we wanted to fix it, we'd likely would have to quirk the implementation on .NET Framework. For .NET Core, we can debate the merits of quirking, but it's likely we break customers with changing the seed.

Thoughts?