Study started since 2011年10月17日 素性测试算法，素性测定(11Y11) primality testing
Quotes from Renowned Mathematicians
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- Bu səhifədəki naviqasiya:
- 2.Keyword
- 3.Introduction
- 6.Structure of Writing
1.Quotes from Renowned MathematiciansDisquisitiones arithmeticae ” Dass die Aufgabe, die Primzahlen von den zusammengesetzten zu unterscheiden [. . . ] zu den wichtigsten und n¨utzlichsten der gesamten Arithmetik geh¨ort [. . . ] ist so bekannt, dass es ¨uberfl¨ussig w¨are, hier ¨uber viele Worte zu verlieren. “ Carl Friedrich Gauß (1801) Carl Friedrich Gauß (1777{1855): "Zahlentheorie ist die Königin der Mathematik. Mathematics is the queen of sciences and arithmetic the queen of mathematics Carl Friedrich Gauss The problem of distinguishing prime numbers from composite numbers and of resolving the latter into their prime factors is known to be one of the most important and useful in arithmetic. (. . . ) Further, the dignity of the science itself seems to require that every possible means be explored for the solution of a problem so elegant and so celebrated problem be zealously cultivated. Carl Friedrich Gauss « Le problème où l’on se propose de distinguer les nombres premiers des nombres composés, et de résoudre ceux-ci en leurs facteurs premiers, est connu comme l’un des plus importants et des plus utiles de toute l’Arithmétique ; il a sollicité l’industrie et la sagacité des géomètres tant anciens que modernes, à un point tel qu’il serait superflu de discuter en détail à cet égard. [. . . ] « De surcroît, la dignité de la science même semble demander que tous les secours possibles soient explorés avec soin pour parvenir à la solution d’un problème si élégant et si célèbre. »
ad grauissima ac utilissima totius Arithmeticæ pertinere, et geometrarum tum ueterum tum recentiorum industriam ac sagacitatem occupauisse, tam notum est, ut de hac re copiose loqui superfluum foret. [. . . ] « Prætereaque scientiæ dignitas requirere uidetur, ut omnia subsidia ad solutionem problematis tam elegantis ac celebris sedulo excolantur. » Disquisitiones Arithmeticæ de Gauß est, dans le texte latin : Johann Carl Friedrich Gauß, Disquisitiones Arithmeticæ, 329. 2.Keyword素性测试算法
素性测定 page primality prime Prime number testing test prove proving Primzahltests test de primalité nombres premiers Πρώτοι αριθμοί δοκιμές αριθμό проверки простоты чисел Randomized (Probalistic) Provable Primality Testing Deterministic Primality Testing
AKS Primality testing AKS Primality test AKS Prime testing AKS Prime test AKS Primzahltests AKS test de primalité nombres premiers Le test de primalité AKS AKS δοκιμές αριθμό AKS проверки простоты чисел Prime number
3.1.The Aim of Thesis3.2.The Scope of Thesis3.3.Research Hierarchical Diagram4.Related Math Branches or Sub-Disciples5.Presentation Styles用各种IT技术
Short texts Electronically available only Electronic formats
Easy to read even for laymen and like lovestory Use as much as drawings, pictures.animations as possible to accompany or replace texts
Drawings 图 三维图标 表 Graphs
Charts Pies
PPT Flash SWF Slides OTHER FORMS OF SLIDES EBOOKS IN CHM, HLP, EXE OR OTHERS Movies and Animations 3D VRML FLASH MOVIES web audio and video streaming QUICKTIME REALMEDIA WINDOWSMEDIA WEB PORTAL web incl web2.0 html php
java SOFTWARE DATABASE MOBILE AND HANDHELD DEVICES DVD/VCDS USB 网络多媒体
multimedia) 6.Structure of WritingNewton or Euclid styles Give every definiyion, axiom, proposition, theorem, corrolary etc a serial number and a name conventions or notations Common Notions
Terms
Terminology Etymology Encyclopedia Glossary
Lexicon Nomenclature Abbreviations List of Symbols Index
Principles Assertion Assumptions Hypothesis Conjecture Suggestion Common Notions Fact Proposition If we can prove a statement true, then that statement is called a proposition. a proposition is a less important or less fundamental assertion, Predicates Theory Laws
If a theorem is not particularly interesting, but is useful in proving an interesting statement, then it’s often called a lemma. This one is found in Euclid’s Elements. Sometimes instead of proving a theorem or proposition all at once, we break the proof down into modules; that is, we prove several supporting propositions, which are called lemmas, and use the results of these propositions to prove the main result. a lemma is something that we will use later in this book to prove a proposition or theorem, Statement
Rules
Porism Theorem
a theorem is a deeper culmination of ideas, A theorem is a valid implication of sufficient interest to warrant special attention. If we can prove a proposition or a theorem, we will often, with very little effort, be able to derive other related propositions called corollaries. a corollary is an easy consequence of a proposition, theorem, or lemma. Collonary A corollary is a theorem that logically follows very simply from a theorem. A corollary is a theorem that logically follows very simply from a theorem. Sometimes it follows from part of the proof of a theorem rather than from the statement of the theorem. In any case, it should be easy to see why it’s true.
A corollary is a theorem that logically follows very simply from a theorem. A corollary is a theorem that logically follows very simply from a theorem. Sometimes it follows from part of the proof of a theorem rather than from the statement of the theorem. In any case, it should be easy to see why it’s true. Postulations Scholium Conclusions Consequence Comment Remark Observation Claim Proof Equations Formulas
Caveat Thesis Conics Literature Reference / Bibliography
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