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ID 56015
FullText URL
Author
Shimizu, Kenichi
Abstract
We study a class of integers called SP numbers (Sum Prime numbers). An SP number is by de nition a positive integer d that gives rise to a prime number (a + b)=gcd(4; 1 + d) from every factorization d = ab. We also discuss properties of SP numbers in relations with arithmetic of imaginary quadratic elds (least split primes, exponents of ideal class groups). Further we point out that special cases of SP numbers provide the problems of distribution of prime numbers (twin primes, Sophi-Germain primes, quadratic progressions). Finally, we consider the problem whether there exist in nitely many SP numbers.
Keywords
SP number
prime number
imaginary quadratic fi eld
Note
Mathematics Subject Classi cation. Primary 11A41;Secondary 11R11,11R29
Published Date
2018-01
Publication Title
Mathematical Journal of Okayama University
Volume
volume60
Issue
issue1
Publisher
Department of Mathematics, Faculty of Science, Okayama University
Start Page
155
End Page
164
ISSN
0030-1566
NCID
AA00723502
Content Type
Journal Article
Official Url
http://www.math.okayama-u.ac.jp/mjou/
language
英語
Copyright Holders
Copyright©2018 by the Editorial Board of Mathematical Journal of Okayama University
File Version
publisher
Refereed
True
Submission Path
mjou/vol59/iss1/8