# “Three years of Sundays” – Frank Nelson Cole

I first heard of Frank Nelson Cole a few years ago and about how he figured out one of mysteries in Mathnatics – the Mersenne number M67. M67 is computing increasing powers of 2 and finally subtracting 1. The result was the 21-digit number 147,573,952,589,676,412,927. Édouard Lucas had demonstrated in 1876 that M67 must have factors (i.e., is not prime), but he was unable to determine what those factors were.

Cole was an American mathematician born in 1861, was educated at Harvard. He lectured there and later at the University of Michigan and at Columbia University, New York. He had heard about M67 in college and it always interested him.

On October 31, 1903, Cole famously made a presentation to a meeting of the American Mathematical Society where he identified the factors of the Mersenne number 267 − 1, or M67.During Cole’s so-called “lecture”, he approached the chalkboard and in complete silence proceeded to calculate the value of M67, with the result being 147,573,952,589,676,412,927. Cole then moved to the other side of the board and wrote 193,707,721 × 761,838,257,287, and worked through the tedious calculations by hand.
Upon completing the multiplication and demonstrating that the result equaled M67, Cole returned to his seat, not having uttered a word during the hour-long presentation. His audience greeted the presentation with a standing ovation. Cole later admitted that finding the factors had taken “three years of Sundays.”
What have you done in the last 3 years on sunday? Let’s say he spent only 3 hours a sunday on this, that is 468 hours. The determination I think is amazing!