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Factorization Of The Tenth Fermat Number
 MATH. COMP
, 1999
"... We describe the complete factorization of the tenth Fermat number F 10 by the elliptic curve method (ECM). F 10 is a product of four prime factors with 8, 10, 40 and 252 decimal digits. The 40digit factor was found after about 140 Mflopyears of computation. We also discuss the complete factor ..."
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Cited by 22 (10 self)
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We describe the complete factorization of the tenth Fermat number F 10 by the elliptic curve method (ECM). F 10 is a product of four prime factors with 8, 10, 40 and 252 decimal digits. The 40digit factor was found after about 140 Mflopyears of computation. We also discuss the complete factorization of other Fermat numbers by ECM, and summarize the factorizations of F 5 ; : : : ; F 11 .
Two new factors of Fermat numbers
, 1997
"... Abstract. We report the discovery of new 27decimal digit factors of the thirteenth and sixteenth Fermat numbers. Each of the new factors was found by the elliptic curve method. After division by the new factors and other known factors, the quotients are seen to be composite numbers with 2391 and 19 ..."
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Cited by 5 (2 self)
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Abstract. We report the discovery of new 27decimal digit factors of the thirteenth and sixteenth Fermat numbers. Each of the new factors was found by the elliptic curve method. After division by the new factors and other known factors, the quotients are seen to be composite numbers with 2391 and 19694 decimal digits respectively. 1.
Three New Factors of Fermat Numbers
 Math. Comp
, 2000
"... We report the discovery of a new factor for each of the Fermat numbers F 13 ,F 15 ,F 16 . These new factors have 27, 33 and 27 decimal digits respectively. Each factor was found by the elliptic curve method. After division by the new factors and previously known factors, the remaining cofactors are ..."
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Cited by 4 (0 self)
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We report the discovery of a new factor for each of the Fermat numbers F 13 ,F 15 ,F 16 . These new factors have 27, 33 and 27 decimal digits respectively. Each factor was found by the elliptic curve method. After division by the new factors and previously known factors, the remaining cofactors are seen to be composite numbers with 2391, 9808 and 19694 decimal digits respectively. 1.
Integer Factoring
, 2000
"... Using simple examples and informal discussions this article surveys the key ideas and major advances of the last quarter century in integer factorization. ..."
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Cited by 2 (0 self)
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Using simple examples and informal discussions this article surveys the key ideas and major advances of the last quarter century in integer factorization.
A Simpler Sieving Device: Combining ECM and TWIRL
 In Proceedings of ICISC 2006
, 2006
"... A main obstacle in manufacturing the TWIRL device for realizing the sieving step of the Number Field Sieve is the sophisticated chip layout. Especially the logic for logging and recovering large prime factors found during sieving adds significantly to the layout complexity. We describe a device b ..."
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Cited by 2 (1 self)
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A main obstacle in manufacturing the TWIRL device for realizing the sieving step of the Number Field Sieve is the sophisticated chip layout. Especially the logic for logging and recovering large prime factors found during sieving adds significantly to the layout complexity. We describe a device building on the Elliptic Curve Method (ECM) that for parameters of interest allows to replace the complete logging part in TWIRL by an o#wafer postprocessing. The postprocessing is done in real time, leaving the total sieving time basically unchanged.
Computational Methods in Public Key Cryptology
, 2002
"... These notes informally review the most common methods from computational number theory that have applications in public key cryptology. ..."
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Cited by 1 (1 self)
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These notes informally review the most common methods from computational number theory that have applications in public key cryptology.
Integer Factorization Algorithms Illustrated by the Factorization of Fermat Numbers
, 1998
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Factorizations of a^n ± 1, 13 ≤ a < 100: Update 2
, 1996
"... This Report updates the tables of factorizations of a n \Sigma 1 for 13 a ! 100, previously published as CWI Report NMR9212 (June 1992) and updated in CWI Report NMR9419 (September 1994). A total of 760 new entries in the tables are given here. The factorizations are now complete for n ! 67, an ..."
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This Report updates the tables of factorizations of a n \Sigma 1 for 13 a ! 100, previously published as CWI Report NMR9212 (June 1992) and updated in CWI Report NMR9419 (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 . 1991 Mathematics Subject Classification. Primary 11A25; Secondary 1104 Key words and phrases. Factor tables, ECM, MPQS, SNFS To appear as Report NMR96??, Centrum voor Wiskunde en Informatica, Amsterdam, March 1996. Copyright c fl 1996, the authors. Only the front matter is given here. For the tables, see rpb134u2.txt . rpb134u2 typeset using L a T E X 1 Introduction For many years there has been an interest in the prime factors of numbers of the form a n \Sigma 1, where a is a small integer (the base) and n is a positive exponent. Such numbers often arise. For example, if a is prime then there is a finite field F with a n ...
Factorizations of a^n±1, 13 ≤ a < 100: Update 2
"... This Report updates the tables of factorizations of a 1 for 13 a < 100, previously published as CWI Report NMR9212 (June 1992) and updated in CWI Report NMR9419 (September 1994). A total of 760 new entries in the tables are given here. The factorizations are now complete for n < 67, and th ..."
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This Report updates the tables of factorizations of a 1 for 13 a < 100, previously published as CWI Report NMR9212 (June 1992) and updated in CWI Report NMR9419 (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 .