| ID | 56015 |
| FullText URL | |
| Author |
Shimizu, Kenichi
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| 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.
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| Keywords | SP number
prime number
imaginary quadratic fi eld
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| Note | Mathematics Subject Classi cation. Primary 11A41;Secondary 11R11,11R29
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| Published Date | 2018-01
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| Publication Title |
Mathematical Journal of Okayama University
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| Volume | volume60
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| Issue | issue1
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| Publisher | Department of Mathematics, Faculty of Science, Okayama University
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| Start Page | 155
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| End Page | 164
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| ISSN | 0030-1566
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| NCID | AA00723502
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| Content Type |
Journal Article
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| Official Url | http://www.math.okayama-u.ac.jp/mjou/
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| language |
English
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| Copyright Holders | Copyright©2018 by the Editorial Board of Mathematical Journal of Okayama University
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| File Version | publisher
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| Refereed |
True
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| Submission Path | mjou/vol59/iss1/8
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