ID | 56015 |
フルテキストURL | |
著者 |
Shimizu, Kenichi
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抄録 | We study a class of integers called SP numbers (Sum Prime numbers). An SP number is by denition 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 innitely many SP numbers.
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キーワード | SP number
prime number
imaginary quadratic field
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備考 | Mathematics Subject Classication. Primary 11A41;Secondary 11R11,11R29
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発行日 | 2018-01
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出版物タイトル |
Mathematical Journal of Okayama University
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巻 | 60巻
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号 | 1号
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出版者 | Department of Mathematics, Faculty of Science, Okayama University
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開始ページ | 155
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終了ページ | 164
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ISSN | 0030-1566
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NCID | AA00723502
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資料タイプ |
学術雑誌論文
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オフィシャル URL | http://www.math.okayama-u.ac.jp/mjou/
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言語 |
英語
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著作権者 | Copyright©2018 by the Editorial Board of Mathematical Journal of Okayama University
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論文のバージョン | publisher
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査読 |
有り
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Submission Path | mjou/vol59/iss1/8
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