منابع مشابه
Evaluation of Certain Legendre Symbols
We state and prove an apparently hitherto unrecorded evaluation of certain Legendre symbols: if p is prime, p 6= 2, and ab = p − 1, then the Legendre symbol ( b p ) is given by ( b p ) = (−1).
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For any real x, the most common difference that occurs among the consecutive primes less than or equal to x is called a jumping champion. This term was introduced by J. H. Conway in 1993. There are occasionally ties. Therefore there can be more than one jumping champion for a given x. The first, but short-lived, jumping champion is 1. Aside from the numerical studies, nothing else has been prov...
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Let G(x) denote the largest gap between consecutive grimes below x, In a series of papers from 1935 to 1963, Erdos, Rankin, and Schonhage showed that G(x) :::: (c + o( I)) logx loglogx log log log 10gx(loglog logx) -2, where c = eY and y is Euler's constant. Here, this result is shown with c = coeY where Co = 1.31256... is the solution of the equation 4/ Co e -4/co = 3 . The principal new tool ...
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2 . Admissible constellations . Let us start with a formal definition : al, 122, . . ., ak is an admissible sequence of integers if the ai's do notform a complete set of residues mod p for any prime p.-Clearly only the primes p 5 k have to be considered . A sequence which is not admissible is called inadmissible . Beginning with the admissible sequence (ai) we now search for constellations of i...
متن کاملOn the Difference of Consecutive Primes
is greater than (c2/2)n. A simple calculation now shows that the primes satisfying (4) also satisfy the first inequality of (3) i΀ = e(ci) is chosen small enough. The second inequality of (3) is proved in the same way, which proves Theorem 2. Further, we obtain, as an immediate corollary of Theorem 1, that Received by the editors October 17, 1947. 1 P. Erdös and P. Turân, Some new questions on...
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 2019
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa170810-29-11