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References (13)
-
Patrick Hough (2016)
A lower bound for biases amongst products of two primesResearch in Number Theory, 3
-
M. Mkaouar, W. Wannes (2016)
On the normal number of prime factors of φ(n) subject to certain congruence conditionsJournal of Number Theory, 160
-
PL Chebyshev (1853)
Lettre de M. le professeur Tchébyshev à M. Fuss, sur un nouveau théorème relatif aux nombres premiers contenus dans la formes 4n + 1 et 4n + 3Bull. de la Classe phys.-math. de lAcad. Imp. des Sciences St. Petersburg, 11
-
M. Drmota, C. Mauduit, J. Rivat (2009)
Primes with an average sum of digitsCompositio Mathematica, 145
-
C. Mauduit, Joël Rivat (2010)
Sur un problème de Gelfond: la somme des chiffres des nombres premiersAnnals of Mathematics, 171
-
A. Granville, G. Martin (2004)
Prime Number RacesThe American Mathematical Monthly, 113
-
D. Dummit, A. Granville, H. Kisilevsky (2014)
Big biases amongst products of two primesarXiv: Number Theory
-
(1853)
Lettre de M -
A. Gelfond (1968)
Sur les nombres qui ont des propriétés additives et multiplicatives donnéesActa Arithmetica, 13
-
(1975)
Sur les fonctions Q-multiplicatives et Q-additives, Thèse 3me cycle, Orsay -
Publisher's Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations -
PL Chebyshev (1853)
208Bull. de la Classe phys.-math. de lAcad. Imp. des Sciences St. Petersburg, 11
-
(1896)
Recherches analytiques sur la théorie des nombres premiers
- Publisher
- Springer Journals
- Copyright
- Copyright © Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2021
- ISSN
- 0126-6705
- eISSN
- 2180-4206
- DOI
- 10.1007/s40840-021-01209-5
- Publisher site
- See Article on Publisher Site
Abstract
Let g⩾2\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$g \geqslant 2$$\end{document} be an integer and Sg(n)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$S_g(n)$$\end{document} denote the sum of the digits in base g of the positive integer n. We obtain asymptotic formulas for the number of odd integers up to x that can be written as a product pq, with p, q both primes, satisfy Sg(p)≡Sg(q)≡amodb(b⩾2,a∈Z)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$S_g(p) \equiv S_g(q) \equiv a ~\mathrm{mod}\,~ b\ (b \geqslant 2, a \in {\mathbb {Z}})$$\end{document}. So, we observe a large bias amongst such integers.
Journal
Bulletin of the Malaysian Mathematical Sciences Society – Springer Journals
Published: Mar 1, 2022
Keywords: Large bias; Prime number; Sum of digits function; 11A63; 11L03; 11N05; 11N69