This paper introduces the Mersenne Twister (MT), a new pseudorandom number generator with a super astronomical period of $2^{19937}-1$ and 623-dimensional equidistribution up to 32 bits accuracy. The MT is a variant of the previously proposed TGFSR generator, modified to admit a Mersenne-prime period. It uses a characteristic polynomial with many terms and efficient algorithms for polynomial calculations over the two-element field. The generator is implemented as a portable C-code (MT19937) that passed stringent statistical tests, including the diehard test, and is comparable in speed to other modern generators. The MT's performance is attributed to its efficient algorithms and unique properties in polynomial algebra over the two-element field. The paper also discusses the k-distribution, a measure of randomness, and the primitivity of the characteristic polynomial, which is tested using an inversive-decimation method. The MT is shown to have excellent k-distribution properties and is one of the most promising pseudorandom number generators at the present time. The paper concludes that the MT's performance is due to its efficient algorithms and unique properties in polynomial algebra over the two-element field.This paper introduces the Mersenne Twister (MT), a new pseudorandom number generator with a super astronomical period of $2^{19937}-1$ and 623-dimensional equidistribution up to 32 bits accuracy. The MT is a variant of the previously proposed TGFSR generator, modified to admit a Mersenne-prime period. It uses a characteristic polynomial with many terms and efficient algorithms for polynomial calculations over the two-element field. The generator is implemented as a portable C-code (MT19937) that passed stringent statistical tests, including the diehard test, and is comparable in speed to other modern generators. The MT's performance is attributed to its efficient algorithms and unique properties in polynomial algebra over the two-element field. The paper also discusses the k-distribution, a measure of randomness, and the primitivity of the characteristic polynomial, which is tested using an inversive-decimation method. The MT is shown to have excellent k-distribution properties and is one of the most promising pseudorandom number generators at the present time. The paper concludes that the MT's performance is due to its efficient algorithms and unique properties in polynomial algebra over the two-element field.