Development of Fast Deterministic Primarity Testing Algorithms Based on Pseudosquares

• Project/Area Number: 24650007
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: Fundamental theory of informatics
• Research Institution: Okayama University
• Principal Investigator: JIMBO Shuji 岡山大学, 自然科学研究科, 講師 (00226391)
• Project Period (FY): 2012-04-01 – 2016-03-31
• Project Status: Completed (Fiscal Year 2015)
• Budget Amount: ¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000); Fiscal Year 2014: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2012: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
• Keywords: 疑似平方数 / 素数判定 / アルゴリズム理論 / 素数判定アルゴリズム / グラフ理論 / アルゴリズム / 巡回的グラフ / 整数計画ソルバ / カーマイケル数

Outline of Final Research Achievements

Pseudosquares are integers that satisfy conditions obtained by extending the ones that square numbers satisfy. A conjecture that asserts relations between a condition used in a fast deterministic primarity testing algorithm based on huge pseudosquares and Carmichael numbers has been proposed. It is hard to determine that a Carmichael number is not a prime number by the Fermat test. The conjecture proposed does not directly accelerate deterministic primarity testing algorithms. However, development of theoretical research on pseudosquares is expected.

Research Products

• [Journal Article] A proposal of an index to the graph isomorphism based on the structural square of a graph (2015)
  • Author(s): Shuji Jimbo and Yuki Nakagawa
  • Journal Title: 数理解析研究所講究録 Volume: 1964 Pages: 180-182
  • Open Access
• [Presentation] ペンタゴの完全解析結果に基づいた完全プレーヤーの設計 (2015)
  • Author(s): 神保秀司・小林祐貴
  • Organizer: 第14回情報科学技術フォーラム
  • Place of Presentation: 愛媛大学城北キャンパス (愛媛県松山市)
  • Year and Date: 2015-09-15
• [Presentation] Improvement of the Upper Bound on the Eulerian Recurrent Lengths of Complete Graphs (2015)
  • Author(s): Shuji JIMBO and Akira MARUOKA
  • Organizer: Proceedings of the 9th Hungarian-Japanese Symposium on Discrete Mathematics and Its Applications
  • Place of Presentation: 九州大学西新プラザ (福岡県福岡市)
  • Year and Date: 2015-06-02
  • Int'l Joint Research
• [Presentation] 疑似平方数に基づいた素数判定とカーマイケル数との関係 (2012)
  • Author(s): 神保 秀司
  • Organizer: 第11回情報科学技術フォーラム (電子情報通信学会・情報処理学会共催)
  • Place of Presentation: 法政大学小金井キャンパス (東京都)