# Factors of Mersenne Number M67/Historical Note

## 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 $1903$.

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.*

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.

## Sources

- 1951: Eric Temple Bell:
*Mathematics: Queen and Servant of Science* - 1986: David Wells:
*Curious and Interesting Numbers*... (previous) ... (next): $2^{67} - 1$ - 1992: George F. Simmons:
*Calculus Gems*... (previous) ... (next): Chapter $\text {A}.12$: Mersenne ($\text {1588}$ – $\text {1648}$) - 1997: David Wells:
*Curious and Interesting Numbers*(2nd ed.) ... (previous) ... (next): $2^{67} - 1$