Development of Fast Deterministic Primarity Testing Algorithms Based on Pseudosquares
| Project/Area Number |
24650007
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Multi-year Fund |
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| Research Field |
Fundamental theory of informatics
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| Research Institution | Okayama University |
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Principal Investigator |
JIMBO Shuji 岡山大学, 自然科学研究科, 講師 (00226391)
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| Project Period (FY) |
2012-04-01 – 2016-03-31
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| Project Status |
Completed (Fiscal Year 2015)
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| Budget Amount *help |
¥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)
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| 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 |
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| 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.
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Report
(5 results)
Research Products
(4 results)
