2 |
67 |
– 1 is Composite! |
In 1903 at a meeting of the American Mathematical Society, among the speakers on the agenda was Frank Nelson Cole. When it came Cole’s turn, he purposefully walked to the front of the room and without saying anything, proceeded to multiply 2 by itself 67 times under his breath. He then subtracted 1 and finally arrived at the enormous result of 147,573,952,588,676,412,927. Having witnessed this wordless calculation, the bemused audience then watched as he wrote on the blackboard
761,838,257,287which he also computed silently.
The product was none other than
Cole then took his seat without uttering a word. Those in the audience, having just witnessed the explicit factorisation of Mersenne's number 267 – 1 into its two huge factors, then burst into unanimous applause for Cole and gave him a standing ovation.
It was not for a while after the meeting until Cole admitted he had been working on the calculation for the previous two decades!
In spite of Cole’s factorisation, Mersenne numbers remain a plentiful source of primes. In fact the five largest primes known today are Mersenne primes. For more information on the current search for primes see