• Corpus ID: 124941778

Factorizations of $ a ^ n $ + 1, 13 < a < 100 : update 2

@article{Brent1996FactorizationsO,
  title={Factorizations of \$ a ^ n \$ + 1, 13 < a < 100 : update 2},
  author={Richard P. Brent and Peter L. Montgomery and Herman J. J. te Riele and Henk Boender and M. Elkenbracht-Huizing and Paul C. Leyland and A. Muller and Mullfac and Robert D. Silverman and T Sosnowski},
  journal={Report - Department of Numerical Mathematics},
  year={1996},
  pages={1-42}
}
textabstractThis Report (NM-R9609, March 1996) updates the tables of factorizations of $a^n pm 1$ for $13 le a < 100$, previously published as CWI Report NM-R9212 (June 1992) and updated in CWI Report NM-R9419 (September 1994). A total of 760 new entries in the tables are given here. The factorizations are now complete for $n < 67$, and there are no composite cofactors smaller than $10^{94$. 
ir.cwi.nl

References

SHOWING 1-10 OF 34 REFERENCES

Update 1 to: factorizations of an±1, 13≤a<100

In an earlier Report (NM-R9212, June 1992), two of us gave tables of factoriza-tions of a n 1 for 13 a < 100. The exponents n satissed a n < 10 255 if a < 30, and n 100 if a 30. The factorizations…

FACTORIZATIONS OF a n ± 1, 13 a < 100

As an extension of the “Cunningham” tables [4, 5] we present tables of factorizations of a n ± 1 for 13 a < 100. The exponents n satisfy a n < 10 255 if a < 30, and n 100 if a 30. The factorizations…

Speeding the Pollard and elliptic curve methods of factorization

Since 1974, several algorithms have been developed that attempt to factor a large number N by doing extensive computations module N and occasionally taking GCDs with N. These began with Pollard's p 1…

Factor: an integer factorization program for the IBM PC

Factor is a program which accesses a large database of factors of integers of the form a±1. As of March 1994 the database contains more than 175,000 factors of size at least 10. The program factor…

Factoring Integers with Large-Prime Variations of the Quadratic Sieve

Experiments show that for the Cray C90 implementations PPMPQS beats PMPZS for numbers of more than 80 digits, and that this crossover point goes down with the amount of available central memory.

A survey of modern integer factorization algorithms

Introduction An integer n is said to be a prime number or simply prime if the only divisors of n are and n There are in nitely many prime numbers the rst four being and If n and n is not prime then n…

Tables of Fibonacci and Lucas factorizations

We list the known prime factors of the Fibonacci numbers Fn for n < 999 and Lucas numbers Ln for n < 500. We discuss the various methods used to obtain these factorizations, and primality tests, and…

An FFT extension of the elliptic curve method of factorization

This thesis describes how to apply convolutions modulo N and last polynomial arithmetic algorithms in the search of factors of a large integer N, which effectively increases the range of ECM by a factor of 100 with about twice the combined Step 1/Step 2 execution time previously required.

The multiple polynomial quadratic sieve

A modification, due to Peter Montgomery, of Pomerance's Quadratic Sieve for factoring large integers is discussed along with its implementation, which enables one to factor numbers in the 60-digit range in about a day, using a large minicomputer.

Factoring integers with elliptic curves

This paper is devoted to the description and analysis of a new algorithm to factor positive integers that depends on the use of elliptic curves and it is conjectured that the algorithm determines a non-trivial divisor of a composite number n in expected time at most K( p)(log n)2.