Yes, I am aware that MT19937 is not perfect and also that it is not good enough for cryptography. But : almost all math packages are using it. For most Monte-Carlo programs : it is quite sufficiently random. It passes many tests including hard ones and Knuth criteria. You need a pretty high level of randomness to find the limits of this monster. I think that this kind of <discussion> has already occurred many times for random number generators. There is a saying in this area (Von Neumann) : Anyone who attempts to generate random numbers by deterministic means is, of course, living in a state of sin. Best regards, Simon Plouffe Le 2021-01-31 à 02:49, Fred Lunnon a écrit :
<< The Mersenne Twister is a procedure to produce very good random numbers. >>
However, for a more nuanced view see https://arxiv.org/pdf/1910.06437.pdf
WFL
On 1/31/21, Simon Plouffe <simon.plouffe@gmail.com> wrote:
Hello, this is also true in base 10. But with conditions. The period needs to be even. For primes it is always true (if the period is even).
1/7 = 0.142857 and 142 + 857 = 999.
Numbers have to be to a multiple of 2 or 5 within the factorization.
1/323 in base 10 has 144 digits from which the first 72 are complement to the other half, 323 = 17*19.
Important remark : If you take any integer m and if you can tell which half you are or another way of saying it : if you can tell where the half period is : this is enough information to factor m. Of course, a number m of let's say 300 digits could have a very long period when we compute 1/m.
This fact was taken into account when they constructed the Mersenne Twister by using the period of 2^19937 -1. It has 10^6002 digits. The Mersenne Twister is a procedure to produce very good random numbers. So good that these days, most of the serious math programs uses it . (even excel and microsoft).
Best regards, Simon Plouffe
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