Factors of Mersenne Number M67/Historical Note

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Historical Note on Factors of Mersenne Number $M_{67}$

The Factors of Mersenne Number $M_{67}$ were demonstrated by Frank Nelson Cole in a famously dramatic presentation On The Factorization of Large Numbers to a meeting of the American Mathematical Society in October $1903$.

It is noted that Marin Mersenne had originally listed $M_{67}$ as one of the integers of the form $2^p - 1$ to be prime.

When called to give his lecture, he walked to the blackboard, and worked out the calculation, longhand, of $2^{67}$. Then he carefully subtracted $1$.

Moving to another area of the board, he then multiplied out $193, 707, 721 \times 761, 838, 257, 287$.

The numbers matched.

Cole returned to his seat to thunderous applause, having delivered the only lecture in history in which not a word was spoken.


When asked how long it had taken him to find these factors, he reportedly replied:

Three years of Sundays.


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