He and Schönhage refined and published the method in 1971. In 1968 Strassen discovered how to multiply quickly using Fast Fourier Transforms. More recently, the search has demanded new and faster ways of multiplying large integers. They left in their wake some of the greatest theorems of elementary number theory (such as Fermat's little theorem and quadratic reciprocity). In the tradition section above I listed some of the giants who were in the search (such as Euclid, Euler and Fermat). The same is true for the quest for record primes. By-products such as the new technologies and materials that were developed for the race that are now common everyday items, and the improvements to education's infrastructure that led many man and women into productive lives as scientists and engineers. For the by-products of the quest.īeing the first to put a man on the moon had great political value for the United States of America, but what was perhaps of the most lasting value to the society was the by-products of the race. ) In short, the tradition of seeking large primes (especially the Mersennes) has been long and fruitful It is a tradition well worth continuing. (Look, for example, at the concepts required to develop simple proofs such as or. Much of elementary number theory was developed while deciding how to handle large numbers, how to characterize their factors and discover those which are prime. How can we resist joining such an illustrious group? Large primes (especially of this form) were then studied (in chronological order) by Cataldi, Descartes, Fermat, Mersenne, Frenicle, Leibniz, Euler, Landry, Lucas, Catalan, Sylvester, Cunningham, Pepin, Putnam and Lehmer (to name a few). So the quest for these jewels began near 300 BC. He realized that the even perfect numbers ( no odd perfect numbers are known) are all closely related to the primes of the form 2ᴾ-1 for some prime p (now called Mersennes). His goal was to characterize the even perfect numbers (numbers like 6 and 28 which are equal to the sum of their aliquot divisors: 6 = 1+2+3, 28=1+2+4+7+14). Euclid may have been the first to define primality in his Elements approximately 300 BC.
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