Development of Fast Deterministic Primarity Testing Algorithms Based on Pseudosquares

2015 Fiscal Year Final Research Report

• 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
• Keywords: 疑似平方数 / 素数判定 / アルゴリズム理論

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.

Free Research Field

理論計算機科学