The Skewes Number for Twin Primes: Counting Sign Changes of pi 2(x) - C2Li2(x)

• Autorzy: Wolf M.
• Języki publikacji: EN

Abstrakty

EN

The results of computer investigation of the sign changes of the difference between the number of twin primes pi2 (x) and the Hardy-Littlewood conjecture C2Li2 (x) are reported. It turns out that d2 (x) = pi2 (x) - C2Li2 (x) changes the sign at unexpectedly low values of x and for x less than 248 = 2.81... x 1014 there are 477118 sign changes of this difference. It is conjectured that the number of sign changes of d2 (x) for x element of (1, T ) is given by T log(T). The running logarithmic densities of the sets for which d2 (x) greather than 0 and d2 (x) less than 0 are plotted for x up to 2 48.

Słowa kluczowe

EN

primes; twins; Skewes number

• Wydawca: Institute of Bioorganic Chemistry Scientific Publishers OWN, Polish Academy of Sciences
• Czasopismo: Computational Methods in Science and Technology
• Rocznik: 2011
• Tom: Vol. 17, No. 1-2
• Strony: 87--92
• Opis fizyczny: Bibliogr. 33 poz., rys.

Twórcy

autor

Wolf M.

• Group of Mathematical Methods in Physics University of Wrocław Pl. Maxa Borna 9, PL-50-204 Wrocław, Poland,

Bibliografia

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