Tuesday, June 4, 2013

2^67- 1, approximately 1.4757395258968 x 10^20, approximately 148 quintillion

2^67- 1,  approximately 1.4757395258968 x 10^20, approximately 148 quintillion

For many years, people did not know whether this number was prime or composite.

In 1879, Édouard Lucas proved that it was not prime, but was not able to give any factors.

In October 1903, at a meeting of the American Mathematical Society, Frank Nelson Cole was scheduled to deliver a talk called “On the Factorization of Large Numbers”. For his presentation, he walked up to the chalkboard and worked out by hand 2 to the 67th power, then subtracted 1. Then he moved over to a blank spot on the board and worked out in longhand 193,707,721 x 761,838,257,287. The two results matched. Cole sat down. It had been an hour long presentation. This was the only time the audience at an AMS audience vigorously applauded. Later, when asked how long it took him to find the factorization, Cole replied “Three Years of Sundays”.


  1. It is fascinating to me that there are people who devote themselves to figuring out things like this. It makes the world a much more interesting place to me.

  2. Though I DO have to wonder how much less a time it would've taken if he had been fortified with pastrami sandwiches for meals...