# Mersenne Primes

In 1653, Marin Mersenne, of Mersenne Primes fame, made the bold claim that \(2^{67}-1\) was a prime number. That claim remained unchallenged for 250 years – no computers back then – until…

…in 1903, Frank Nelson Cole of Columbia University delivered a talk with the unassuming title “On the Factorization of Large Numbers” at a meeting of the American Mathematical Society. “Cole – who was always a man of very few words – walked to the board and, saying nothing, proceeded to chalk up the arithmetic for raising 2 to the sixty-seventh power,” recalled Eric Temple Bell, who was in the audience. “Then he carefully sustracted 1 [getting the 21‑digit monstrosity 147,573,952,589,676,412,927]. Without a word he moved over to a clear space on the board and multiplied out, by longhand, \(193,707,721 \times 761,838,257,287\)”

The two calculations agreed. Mersenne’s conjecture – if such it was – vanished into the limbo of mathematical mythology. For the first… time on record, an audience of the American Mathematical Society vigorously applauded the author of a paper delivered before it. Cole took his seat without having uttered a word. Nobody asked him a question.

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Now I know where Professor Felton found his inspiration.

You’ve probably heard of Felton (National Academy of Science, IEEE Past President, NRA sustaining member). My advisor told me later that Felton’s academic peak had come at that now-infamous 1982 Symposium on Data Encryption, when he presented the plaintext of the encrypted challenge message that Rob Merkin had published earlier that year using his “phonebooth packing” trap-door algorithm. According to my advisor, Felton wordlessly walked up to the chalkboard, wrote down the plaintext, cranked out the multiplies and modulus operations by hand, and wrote down the result, which was obviously identical to the encrypted text Merkin had published in CACM. Then, still without saying a word, he tossed the chalk over his shoulder, spun around, drew and put a 158grain semi-wadcutter right between Merkin’s eyes. As the echoes from the shot reverberated through the room, he stood there, smoke drifting from the muzzle of his .357 Magnum, and uttered the first words of the entire presentation: “Any questions?” There was a moment of stunned silence, then the entire conference hall erupted in wild applause. God, I wish I’d been there.

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