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First Occurrence of a Given Gap between Consecutive Primes
, 1997
"... Heuristic arguments are given, that the pair of consecutive primes separated by a distance d appears for the first time at p f (d) ¸ p d exp ` 1 2 q ln 2 (d) + 4d ' . The comparison with the results of the computer search provides the support for the conjectured formula. ..."
Abstract

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Heuristic arguments are given, that the pair of consecutive primes separated by a distance d appears for the first time at p f (d) ¸ p d exp ` 1 2 q ln 2 (d) + 4d ' . The comparison with the results of the computer search provides the support for the conjectured formula.
unknown title
, 2007
"... π n−1/22 n as n →∞. Another interpretation of A(n) is as the number of sign choices + and − such that ±1 ± 1 ± 1 ±···±1=0 ifn is even, ±1 ± 1 ± 1 ±···±1=1 ifn is odd. ..."
Abstract
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π n−1/22 n as n →∞. Another interpretation of A(n) is as the number of sign choices + and − such that ±1 ± 1 ± 1 ±···±1=0 ifn is even, ±1 ± 1 ± 1 ±···±1=1 ifn is odd.