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This video claims that the Mersenne-Twister is based on the Linear Congruential Generator. The math in the Mersenne-Twister original paper is a bit too much for me. I have not seen that claim explicitly made in the wikipedia article for Mersenne-Twister or in some of the other sources I consulted. Is the Mersenne-Twister based on the Linear Congruential Generator? High level, how so?

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No it is not.

MT is based on a twisted generalized feedback shift register. It defined on vector spaces over finite fields, specifically $GF(2)$.

The LCG is based on integer arithmetic over the integers modulo $n,$ say $\mathbb{Z}_n.$

The two algebraic structures are quite different so this statement is false.

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