An Overview of Factoring

  • H. C. Williams

Abstract

During a meeting of the American Mathematical Society in 1903, Cole silently demonstrated, to considerable acclaim, that

267−1=193707721·761838257287,

where each of the two numbers on the right hand side is a prime. This result took him “three years of Sundays” to calculate by hand. Today the factorization of a mere 21 digit number would not occasion any special notice. This is because of the development of very fast computing devices and a concomitant development and refinement of methods of factoring which can, be used on these machines. Recent examples of spetacular factorizations include

2211−1=15193·60272956433838849161·P40,

2256+1 = 1238926361552897·P62,

2267−1=535006138814359·1155685395246619182673033·P39,

where all factors on the right hand side are primes and Px denotes a prime of x decimal digits.

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Copyright information

© Plenum Press, New York 1984

Authors and Affiliations

  • H. C. Williams
    • 1
  1. 1.Department of Computer ScienceUniversity of ManitobaWinnipegCanada

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