On a new property of primes that leads to a generalization of Cramer's conjecture

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I present a new property of prime numbers that leads to a generalization of Cramer's conjecture. The study of the gap between consecutive primes is treated as a special case of the gap between consecutive terms of sequences having a certain property called pseudo equidistribution. Both rigorous as well as heuristic arguments are given in support of the generalized Cramer's conjectures.