## Abstract

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

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 include2

^{67}−1=193707721·761838257287,

where all factors on the right hand side are primes and2

^{211}−1=15193·60272956433838849161·P40,2

^{256}+1 = 1238926361552897·P62,2

^{267}−1=535006138814359·1155685395246619182673033·P39,

*Px*denotes a prime of*x*decimal digits.## Keywords

Large Integer Digit Number Primality Testing Decimal Digit Binary Quadratic Form
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## Copyright information

© Plenum Press, New York 1984