The famous anecdote of the 1903 announcement of the factorization of $2^{67}-1$ by Frank Nelson Cole has recently been discussed, for example in light of the announcement of another "twitter-sized" proof by Andrew Booker that $x^3+y^3+z^3=33$ has a solution.
Although there is already a fantastic breakdown of the story on HSM, and an even further review of the mathematics used by Cole on MathOverflow, I wonder if there's more evidence to be found to shed light on how much, if any, of the Cole story is true.
I'll take it as granted that Cole actually did factor $M_{67}$, because he has a paper to prove it.
The earliest source of the anecdote seems to be E.T. Bell's account from the "Queen of Mathematics" chapter in James Roy Newman's edited The World of Mathematics, Vol. 1.
Bell is silent on how long the multiplication would have taken. But there are other, secondary sources that expand on this. For example, Gridgemen states "Subsequently, in private, Cole said that those few minutes at the blackboard had cost him three years of Sundays." However, Wikipedia (March 19, 2019) states "Cole returned to his seat, not having uttered a word during the hour-long presentation."
Because as far as can be traced the story seems to originate from Bell, many have taken that to establish a prima facie case that the entirety of the story is not to be believed. But, is that harsh to Mr. Bell? A broken clock is right twice a day.
At least one question can be asked and answered:
Granting the necessary parts of the story, how long would it take for Cole to actually to do the multiplication on the blackboard?
Perhaps people would not sit through an hour of silent multiplication as Wikipedia suggests, but would sit through a few minutes, as Gridgemen suggests. My rough guess is that it's closer to ten minutes than an hour.
I will perform the experiment shortly.