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Bertrand's Postulate states that for every integer n ≥ 1 there is at least one prime p such that n < p ≤ 2n. In order to verify this theorm for n < 4000 we do not have to check 4000 cases: The Landau trick says it is sufficient to check that
2, 3, 5, 7, 13, 23, 43, 83, 163, 317, 631, 1259, 2503...