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Abstract: We present the results of many factorization runs with the single and double large prime variations (PMPQS, and PPMPQS, respectively) of the quadratic sieve factorization method on SGI workstations, and on a Cray C90 vectorcomputer. Experiments with 71--, 87--, and 99--digit numbers show that for our Cray C90 implementations PPMPQS beats PMPQS for numbers of more than 80 digits, and this cross--over point goes down with the amount of available central memory. For PMPQS a known theoretical... (Update)
Context of citations to this paper: More
...than MPQS . We do not describe ECM, MPQS or NFS here. The reader should refer to [16, 17, 19] for a general description of ECM, to [2, 23] for MPQS, and to [15, 13, 21] for NFS. A recent survey is [7] The particular implementations of ECM by Brent and Montgomery are...
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BibTeX entry: (Update)
H. Boender and H. J. J. te Riele, Factoring integers with large prime variations of the quadratic sieve, Report NM-R9513, Department of Numerical Mathematics, Centrum voor Wiskunde en Informatica, Amsterdam, July 1995. ftp://ftp.cwi.nl/pub/CWIreports/ NW/NM-R9513.ps.Z . http://citeseer.ist.psu.edu/article/boender95factoring.html More
@misc{ boender95factoring,
author = "H. Boender and H. Riele",
title = "Factoring integers with large prime variations of the quadratic sieve",
text = "H. Boender and H. J. J. te Riele, Factoring integers with large prime variations
of the quadratic sieve, Report NM-R9513, Department of Numerical Mathematics,
Centrum voor Wiskunde en Informatica, Amsterdam, July 1995. ftp://ftp.cwi.nl/pub/CWIreports/
NW/NM-R9513.ps.Z .",
year = "1995",
url = "citeseer.ist.psu.edu/article/boender95factoring.html" }
Citations (may not include all citations):411 Random Graphs (context) - Bollob'as - 1985
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45 On random graphs (context) - Erdos, R'enyi - 1959
43 Factoring with Two Large Primes (context) - Lenstra, Manasse - 1994
39 The Quadratic Sieve Factoring Algorithm (context) - Pomerance - 1985
37 THE MAGIC WORDS ARE SQUEAMISH OSSIFRAGE (context) - Atkins, Graff et al.
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7 A method of factoring and the factorization of (context) - Morrison, Brillhart - 1975
7 An Algorithm for Finding a Fundamental Set of Cycles of a Gr.. (context) - Paton - 1969
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3 A compact algorithm for Gaussian elimination over GF (context) - Parkinson, Wunderlich - 1984
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2 Recherches sur la th'eorie des nombres (context) - Kraitchik - 1929
1 Factorization using the quadratic sieve References 18 algori.. (context) - Davis, Holdridge - 1983
1 Implementation of the Hypercube Variation of the Multiple Po.. - Peralta
1 Faktorisieren mit dem Quadratischen Sieb (context) - Denny - 1993
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