Prime factors k.2n + 1 of Fermat numbers Fm and complete factoring status Compiled by Wilfrid Keller Prime Fermat numbers Completely factored Fermat numbers Factorizations known to be incomplete Composite cofactors Composite Fermat numbers without known factor Prime factors of larger Fermat numbers Summary of factoring status Count of factors according to difference n - m Known search limits ...

Applet that can be used to find 20- or 30-digit factors of numbers up to 1000 digits long ...

Appendix 1. Factorization results since 04 August 1997 - 2, 000 Abstract (Japanese version is here.) These are factorization results of various kind of numbers. I started this project (factorize various numbers under 100 digits) on 1991 using 80286 PC with 80386 (8 MHz) board. Used tools were UBASIC's factorization program (RHO, ECMX, MPQSX). Target numbers are, primorial +/- 1 (products of ...

Factorizations of Cyclotomic Numbers since 21 January 1999 - 20, 000 Whatsnew, history, errata (August 14, 2002) (These results are updating so frequently. Please check every day.) These numbers are under computing. (August 14, 2002) (To avoid duplication, please check above numbers.) old log ('02/05..09) old log ('02/01..04) old log ('01/09..12) old log ('01/05..08) old log ('01/01..04) old log ...

The Sierpinski Problem: Definition and Status In 1960 Waclaw Sierpinski (1882-1969) proved the following interesting result. Theorem . There exist infinitely many odd integers k such that k.2n + 1 is composite for every n 1. A multiplier k with this property is called a Sierpinski number. The Sierpinski problem consists in determining the smallest Sierpinski number. In 1962, John Selfridge ...

Fibonacci and Lucas Factorizations Below are tables of known factorizations of Fibonacci numbers, Fn, and Lucas numbers, Ln, for n Small tables of Fibonacci factorizations n n (144K) Small tables of Lucas factorizations n n (136K) The first composite holes are at F851 and L842. Composite factors are indicated by (C) following the factor. The compact big tables Format of tables Fibonacci (223K) ...

Game for students which teaches divisibility.

The Nrich Maths Project Cambridge, England. Mathematics resources for children, parents and teachers to enrich learning. Published on the 1st of each month. Problems, children's solutions, interactivities, games, articles, news...

Ivars Peterson's MathTrek May 18, 1998 Cubes of Perfection Playing with integers can lead to all sorts of little surprises. A whole number that is equal to the sum of all its possible divisors --including 1 but not the number itself -- is known as a perfect number (see A Perfect Collaboration). For example, the proper divisors of 6 are 1, 2, and 3, and 1 + 2 + 3 equals 6. Six is the smallest ...

K-12 Math Problems, Puzzles, Tips & Tricks Why do the divisibility 'rules' work Explaining: 10, 2, 4, 8, 2^k, 5, 25 - by Ask Dr. Math's Robert L. 'Dr. Rob' Ward Divisibility Rules || 3, 9, 11, 7, 13, 17... || Alternate Test Method || Origin of Many Div. Rules Cindy Smith asks: From: cms@dragon.com (Cindy Smith) To: Dr. Math dr.math@mathforum.org Subject: Factoring Tricks In reading a popular math ...

Factorizations of xy + yx for 1 y x 101 Home News How Status Wanted Results Records Contributors Join us! Reserve Links Contact Welcome to XYYXF project! Integer factorization is one of the most interesting things in computational number theory. First of all it is closely related to cryptography, that's why large networks spend months of CPUtime cracking crypto-keys and number theorists invent ...

Factors for 2n-1 and 2n+1 for 1200 n 10000: List of factors in the Prime95 lowp.txt file format for: Factors for 2^n+1, 1200 Factors for 2^n+1, 1200 for n multiple of four Factors for 2^n-1, 1200 Factors for 2^n-1, for very large prime n, O(107) RELATED SITES: Cunningham Project; ECMNET; GIMPS; Brents table; Factor World. Hitbox counter ...

Return to my Mathematics pages Go to my home page Divisibility Tests Copyright 1999, Jim Loy How do you tell if a number is divisible by 2 If it is an even number (ends in 0, 2, 4, 6, or 8) it is divisible by 2. Another way to tell is to divide by 2, and if there is no remainder, then it is divisible by 2. This test depends heavily upon the base we are using; we use base-10. If the base is 2, ...

Interesting problem about products of two primes of the same size.

Factoring Papers Note: many of these papers come from other web sites. If the location of the paper is not mentioned, then it is stored at our web site. Surveys A Survey of Modern Integer Factorization Algorithms by Peter L. Montgomery (zipped, postscript, 132K) from CWI (ftp://ftp.cwi.nl:/pub/pmontgom). Some Parallel Algorithms for Integer Factorization by Richard Brent (zipped, postscript, ...

Factors of numbers of the form 4^(3^n)+2^(3^n)+1 and 4^(3^n)-2^(3^n)+1.

Furman University Electronic Journal of Undergraduate Mathematics Volume Three: 1997 Apoorva Khare Divisibility Tests Abstract | Postscript File | dvi File Furman University Electronic Journal of Undergraduate Mathematics ...

Problems & Puzzles: Puzzles Puzzle 101. Digital Divisibility Tests For sure you know some of the popular digital divisibility tests of a given number N by another number p, based on certain operations/properties of the decimal digits of N. For the purposes of this puzzle we must understand a divisibility test as a procedure that operates over the decimal digits of N and that reduces the ...

Perfect numbers Number theory index History Topics Index It is not known when perfect numbers were first studied and indeed the first studies may go back to the earliest times when numbers first aroused curiosity. It is quite likely, although not certain, that the Egyptians would have come across such numbers naturally given the way their methods of calculation worked, see for example where ...