Factoring Number Theory Math

Factoring Number Theory Math

Factoring

Factoring numbers is a concept learnt with the introduction of divisibility in schools, yet the process can be exceptionally challenging and difficult. This category addresses topics from the basic divisibility tests to perfection and the general problem of extracting prime factors.

Top: Science: Math: Number Theory: Factoring

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- Aimed at grade school students and teachers, includes course guidelines, worksheets, and factor tables up to 600.
- Factorizations of numbers composed of all the same digit except first and/or last.
- Article about SNFS factorisation of 3^349-1.
- Links to papers on the theory and practice of factoring.
- Online calculator that factorizes large numbers, specified by formula.
- A collaborative project to produce the factorizations of x^y + y^x for 1<y<x<101.
- Sierpinski proved there exist infinitely many odd integers k such that k*2^n+1 is composite for every n. Ray Ballinger coordinates a search to prove or disprove whether k=78557 is the smallest solution.
- Factoring efforts that have been made so far on numbers of the form n!+-1 using ECM factoring.
- Paul Leyland's list of his own and other factorisations.
- Cash prizes for new factors of Fermat numbers Fn, for n = 12 through 22.
- Java applet that can be used to find 20- or 30-digit factors of numbers or numerical expressions up to 1000 digits long. It also computes the number and sum of divisors, the Euler's totient and moebius functions, and the decomposition of the number in a s
- Dedicated to algorithms and computational results on integer factorization. Includes links to papers, downloadable software, and online resources.
- Numbers representative of those used in the RSA cryptosystem are offered for factor attempts with prizes. A Partition List challenge is also provided in order to encourage work on factoring in general.
- An analysis of problems relating to the numbers k.2^n+-1, primes, and factor patterns, including the Sierpinski problem.
- Leonid Durman's Fermat number factoring site and program.
- Announcement of factorization of a 512-bit RSA key using the General Number Field Sieve (GNFS).
- Divisibility, primes and binary numbers.
- F10 = 2^(2^10) + 1 is the 10-th Fermat number. Richard Brent describes his discovery of the two largest factors.
- Triade systems links to papers on the number field sieve.
- A thorough summary of many major factoring methods. Includes some source code on many pages, gentle introductions to the more complex methods and further links.
- Built by a French amateur, E.-O. Carissan, around 1919. Shallit, Williams and Morain include photographs and references to their paper.
- A listing of all the known pairs of numbers, each of which is the sum of the aliquot divisors of the other. Complete for smaller numbers, and extending beyond 200 digits.
- A definition and description of the Anti-Divisor, and some related results.
- Algorithm that finds non-trivial factors of certain numbers of the form a^b +/- 1.

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