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"... Abstract. We give an explicit form of Ingham’s Theorem on primes in the short intervals, and show that there is at least one prime between every two consecutive cubes x 3 and (x + 1) 3 if log log x ≥ 15. 1. ..."

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Abstract. We give an explicit form of Ingham’s Theorem on primes in the short intervals, and show that there is at least one prime between every two consecutive cubes x 3 and (x + 1) 3 if log log x ≥ 15. 1.