Problems & Puzzles: Conjectures Conjecture 7. The Cramer's Conjecture Asking by the inferior limit for the "gap" between consecutive primes, namely, d_{n} = p_{n+1}  p_{n}, one of the first conjectures became from Cramer, who conjectured in 1937 that d_{n} = O((Lnp_{n})^{2}), which means that limit sup { (p_{n+1}  p_{n} )/ (Lnp_{n})^{2}} =1 as n > infinite Later Cramer assumed the Riemann Hypothesis and showed that d_{n} = O(p^{1/2}_{n}.Lnp_{n}), but as the Riemann Hypothesis is another unproved conjecture, the two Cramer statements were and remain unproved. (Ref. 1, p. 253 ; Ref. 2, p. 7) On February 27, 2017, Reza Farhadian wrote:
*** On Dec 25, 2017 Reza Farhadian wrote:
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