The factorisation of 267 - 1

摘要

Frank Nelson Cole (1861-1921), a prominent American mathematician, was long time secretary of the American Mathematical Society (AMS) and editor-in-chief of its Bulletin. Upon his retirement two prizes, one in number theory and one in algebra, were established in his honour by the AMS. Cole is also remembered for a legendary achievement recorded by E. T. Bell in [1]: At the October, 1903 meeting in New York of the American Mathematical Society, Cole had a paper on the program with the modest title "On the factoring of large numbers". When the chairman called on him for his paper, Cole - who was already a man of very few words - walked to the board, and, saying nothing, proceeded to chalk up the arithmetic of raising 2 to the sixty-seven power. Then he carefully subtracted 1. Without a word he moved over to a clear space on the board and multiplied out, by longhand, 193707721 × 761838257287. The two calculations agreed.... For the first and only time on record, an audience of American Mathematical Society vigorously applauded the author of a paper delivered before it. Cole took his seat without having uttered a word. Nobody asked him a question.