Results 11 to 20 of about 5,332 (130)
Gaps of size 2, 4, and (conditionally) 6 between successive odd composite numbers occur infinitely often [PDF]
Notes on Number Theory and Discrete MathematicsThe infinite sequence of gaps (first differences) between successive odd composite numbers contains only the numbers 2, 4, and 6. We prove that, for any natural number k, the sequence of gaps contains infinitely many k-tuplets of consecutive gaps all ...
Joel E. Cohen, Dexter Senft
doaj +1 more source
An Analytic Approximation to the Density of Twin Primes
Recoletos Multidisciplinary Research Journal, 2018 The highly irregular and rough fluctuations of the twin primes below or equal to a positive integer x are considered in this study. The occurrence of a twin prime on an interval [0,x] is assumed to be random.
Dionisel Y. Regalado, Rodel Azura
doaj +1 more source
On the irregularity of the distribution of the sums of pairs of odd primes
International Journal of Mathematics and Mathematical Sciences, 2002 Let P2(n) denote the number of ways of writing n as a sum of two odd primes. We support a conjecture of Hardy and Littlewood concerning P2(n) by showing that it holds in a certain average sense. Thereby showing the irregularity of P2(n).
George Giordano
doaj +1 more source
On mockenhoupt’s conjecture in the Hardy-Littlewood majorant problem [PDF]
Journal of Contemporary Mathematical Analysis, 2013 20 ...
openaire +3 more sources
A Generalization of the Hardy-Littlewood Conjecture
, 2022 See the abstract in the attached pdf.
openaire +4 more sources
Average prime-pair counting formula [PDF]
, 2009 Taking $r>0$, let $\pi_{2r}(x)$ denote the number of prime pairs $(p, p+2r)$ with $p\le x$. The prime-pair conjecture of Hardy and Littlewood (1923) asserts that $\pi_{2r}(x)\sim 2C_{2r} {\rm li}_2(x)$ with an explicit constant $C_{2r}>0$. There seems to
Korevaar, Jaap, Riele, Herman te
core +7 more sources
Properties of the function f(x)=x/π(x)
International Journal of Mathematics and Mathematical Sciences, 2001 We obtain the asymptotic estimations for ∑k=2nf(k) and ∑k=2n1/f(k), where f(k)=k/π(k), k≥2. We study the expression 2f(x+y)−f(x)−f(y) for integers x,y≥2 and as an application we make several remarks in connection with the conjecture of Hardy and ...
Panayiotis Vlamos
doaj +1 more source
THE LOGARITHMICALLY AVERAGED CHOWLA AND ELLIOTT CONJECTURES FOR TWO-POINT CORRELATIONS
Forum of Mathematics, Pi, 2016 Let $\unicode[STIX]{x1D706}$ denote the Liouville function. The Chowla conjecture, in the two-point correlation case, asserts that
TERENCE TAO
doaj +1 more source
The jumping champion conjecture [PDF]
, 2012 An integer $d$ is called a jumping champion for a given $x$ if $d$ is the most common gap between consecutive primes up to $x$. Occasionally several gaps are equally common. Hence, there can be more than one jumping champion for the same $x$.
Andrew H. Ledoan +5 more
core +1 more source
Smooth solutions to the abc equation: the xyz Conjecture [PDF]
, 2011 This paper studies integer solutions to the ABC equation A+B+C=0 in which none of A, B, C has a large prime factor. Set H(A,B, C)= max(|A|,|B|,|C|) and set the smoothness S(A, B, C) to be the largest prime factor of ABC.
Lagarias, Jeffrey C., Soundararajan, K.
core +2 more sources