3 ms·

This is mentioned in one of the William Dunham books, how Cole was presenting at a conference and silently multiplied two by itself 67 times, subtracted one, an

This is mentioned in one of the William Dunham books, how Cole was presenting at a conference and silently multiplied two by itself 67 times, subtracted one, and then multiplied the two factors he'd found and got the same number. And apparently received a standing ovation. Until then, it was not known whether it was prime (it's of the form 2^p-1 with p prime which iirc are potential Mersenne primes)

smegsicle 4y ago
soon to be a major hollywood motion picture
- version_five 4y ago
  I can picture it being the 1903 equivalent to finding a collision in a modern hashing algorithm, or beating RSA or something. So maybe Sneakers (I also wanted to acknowledge I found your comment funny)
- agentwiggles 4y ago
  Admittedly it's quite dramatic when 45 minutes into the movie, Cole forgets whether he's on 2^42 or 2^43 and has to start over.
  - kccqzy 4y ago
    In elementary school having just learned exponentiation several friends of mine and I challenged each other to see who could find 2^64 the fastest. Two among the group independently discovered the classic exponentiation-by-squaring method, even though none of us could prove it right. Cole definitely would not have multiplied by two repeatedly.
    - madcaptenor 4y ago
      For some reason, the first method that came to mind for me was to find 2^60 as (1000 + 24)^6 (or at least I thought it would be until I realized finding powers of 24 wasn't that easy) and then double that seven times. I would guess that Cole found 2^67 by multiple methods, because obviously it would be tragic if it turned out he was factoring the wrong number.
    - Someone 4y ago
      He also would have known the final decimal digit of powers of 2 (starting at 2^1) is 2, 4, 8, 6, 2, 4, 8, 6, 2, 4, 8, 6… So, 2^42 ends with the same digit as 2^38, 2^34, …, 2^2, so its last digit is a 4.
Chinjut 4y ago
Was it not known by the Lucas test to be composite?
- codeflo 4y ago
  Figuring out that a number is composite is sometimes a lot easier than actually factoring it (see RSA encryption).
svat 4y ago
Yeah this story originates from E. T. Bell, who I'm now fairly convinced just… made it up. (Possibly based on a kernel of truth about the conference presentation involving a lot of calculation, and ending in applause.) He is known for doing that sort of thing. (And Mersenne's list was already known to be inaccurate because of missing M_61 which is prime, and this number M_67 had been independently declared composite by Fauqembergue in 1894 and by Lucas, so was already believed to be composite.)
- antognini 4y ago
  E. T. Bell also has an amusing story about Condorcet. Condorcet was a French aristocrat and during the Revolution had to disguise himself as a commoner to escape France. However, when he was stopping at an inn, the innkeeper asked him how many eggs he would like in his omelette. An an aristocrat, he had no idea how many eggs went into an omelette so he said a dozen, thereby outing himself and ending up in prison. But as far as I can tell, Bell just made that story up, too.
  - svat 4y ago
    Great story, thank you :) This one seems to precede Bell's writing, though: it's mentioned in the 1911 Britannica biography https://en.wikisource.org/wiki/1911_Encyclop%C3%A6dia_Britannica/Condorcet,_Marie_Jean_Antoine_Nicolas_Caritat,_Marquis_de https://en.wikisource.org/wiki/1911_Encyclop%C3%A6dia_Britan... and this 1905 book: https://www.gutenberg.org/files/24492/24492-h/24492-h.htm https://www.gutenberg.org/files/24492/24492-h/24492-h.htm so it may be older.
    - eesmith 4y ago
      The 1902 Britannica as well - https://archive.org/details/encyclopaediabri06kell/page/254/mode/2up?q=+omelette https://archive.org/details/encyclopaediabri06kell/page/254/... . Also, October 29, 1896 "The Youth's Companion" p 583 at https://archive.org/details/sim_youths-companion_1896-10-29_70_44/page/582/mode/2up?q=Condorcet+eggs+omelette https://archive.org/details/sim_youths-companion_1896-10-29_... . The details have changed a bit from the Britannica story. That in turn cites Edith Lichel's 1895 "The Story of Two Salons." https://archive.org/details/storytwosalons00sichgoog/page/n148/mode/2up?q=omelette https://archive.org/details/storytwosalons00sichgoog/page/n1... , which does not give further citations. The Britannica biography says 'On the evening of the 7th April 1794 — not, as Carlyle says, on a " bleared May morning,"'. Using Carlyle" and "bleared May morning" as search terms finds it comes from "The French Revolution" by Thomas Carlyle, first published in 1837. However, while that does describe the story of how Condorcet was identified, it does not mention omelettes or eggs only "asks breakfast". Quoting https://archive.org/details/frenchrevolutio16carlgoog/page/n378/mode/2up?q=condorcet https://archive.org/details/frenchrevolutio16carlgoog/page/n... > Condorcet has lurked deep, these many months; Argus-eyes watching and searching for him. His concealment is become dangerous to others and himself; he has to fly again, to skulk, round Paris, in thickets and stone-quarries. And so at the Village of Clamars, one bleared May morning, there enters a Figure, ragged, rough-bearded, hunger-stricken; asks breakfast in the tavern there. Suspect, by the look of him! "Servant out of place, sayest thou?" Committee-President of Forty-Sous finds a Latin Horace on him: "Art thou not one of those Ci-devants that were wont to keep servants? Suspect!" He is haled forthwith, breakfast unfinished, towards Bourg-la-Reine, on foot: he faints with exhaustion; is set on a peasant's horse; is flung into his damp prison-cell: on the morrow, recollecting him, you enter; Condorcet lies dead on the floor. They die fast, and disappear: the Notabilities of France disappear, one after one, like lights in a Theatre, which you are snuffing out.

smegsicle 4y ago

soon to be a major hollywood motion picture

version_five 4y ago
I can picture it being the 1903 equivalent to finding a collision in a modern hashing algorithm, or beating RSA or something. So maybe Sneakers (I also wanted to acknowledge I found your comment funny)
agentwiggles 4y ago
Admittedly it's quite dramatic when 45 minutes into the movie, Cole forgets whether he's on 2^42 or 2^43 and has to start over.
- kccqzy 4y ago
  In elementary school having just learned exponentiation several friends of mine and I challenged each other to see who could find 2^64 the fastest. Two among the group independently discovered the classic exponentiation-by-squaring method, even though none of us could prove it right. Cole definitely would not have multiplied by two repeatedly.
  - madcaptenor 4y ago
    For some reason, the first method that came to mind for me was to find 2^60 as (1000 + 24)^6 (or at least I thought it would be until I realized finding powers of 24 wasn't that easy) and then double that seven times. I would guess that Cole found 2^67 by multiple methods, because obviously it would be tragic if it turned out he was factoring the wrong number.
  - Someone 4y ago
    He also would have known the final decimal digit of powers of 2 (starting at 2^1) is 2, 4, 8, 6, 2, 4, 8, 6, 2, 4, 8, 6… So, 2^42 ends with the same digit as 2^38, 2^34, …, 2^2, so its last digit is a 4.

Chinjut 4y ago

Was it not known by the Lucas test to be composite?

codeflo 4y ago
Figuring out that a number is composite is sometimes a lot easier than actually factoring it (see RSA encryption).

svat 4y ago

Yeah this story originates from E. T. Bell, who I'm now fairly convinced just… made it up. (Possibly based on a kernel of truth about the conference presentation involving a lot of calculation, and ending in applause.) He is known for doing that sort of thing. (And Mersenne's list was already known to be inaccurate because of missing M_61 which is prime, and this number M_67 had been independently declared composite by Fauqembergue in 1894 and by Lucas, so was already believed to be composite.)

antognini 4y ago
E. T. Bell also has an amusing story about Condorcet. Condorcet was a French aristocrat and during the Revolution had to disguise himself as a commoner to escape France. However, when he was stopping at an inn, the innkeeper asked him how many eggs he would like in his omelette. An an aristocrat, he had no idea how many eggs went into an omelette so he said a dozen, thereby outing himself and ending up in prison. But as far as I can tell, Bell just made that story up, too.
- svat 4y ago
  Great story, thank you :) This one seems to precede Bell's writing, though: it's mentioned in the 1911 Britannica biography https://en.wikisource.org/wiki/1911_Encyclop%C3%A6dia_Britannica/Condorcet,_Marie_Jean_Antoine_Nicolas_Caritat,_Marquis_de https://en.wikisource.org/wiki/1911_Encyclop%C3%A6dia_Britan... and this 1905 book: https://www.gutenberg.org/files/24492/24492-h/24492-h.htm https://www.gutenberg.org/files/24492/24492-h/24492-h.htm so it may be older.
  - eesmith 4y ago
    The 1902 Britannica as well - https://archive.org/details/encyclopaediabri06kell/page/254/mode/2up?q=+omelette https://archive.org/details/encyclopaediabri06kell/page/254/... . Also, October 29, 1896 "The Youth's Companion" p 583 at https://archive.org/details/sim_youths-companion_1896-10-29_70_44/page/582/mode/2up?q=Condorcet+eggs+omelette https://archive.org/details/sim_youths-companion_1896-10-29_... . The details have changed a bit from the Britannica story. That in turn cites Edith Lichel's 1895 "The Story of Two Salons." https://archive.org/details/storytwosalons00sichgoog/page/n148/mode/2up?q=omelette https://archive.org/details/storytwosalons00sichgoog/page/n1... , which does not give further citations. The Britannica biography says 'On the evening of the 7th April 1794 — not, as Carlyle says, on a " bleared May morning,"'. Using Carlyle" and "bleared May morning" as search terms finds it comes from "The French Revolution" by Thomas Carlyle, first published in 1837. However, while that does describe the story of how Condorcet was identified, it does not mention omelettes or eggs only "asks breakfast". Quoting https://archive.org/details/frenchrevolutio16carlgoog/page/n378/mode/2up?q=condorcet https://archive.org/details/frenchrevolutio16carlgoog/page/n... > Condorcet has lurked deep, these many months; Argus-eyes watching and searching for him. His concealment is become dangerous to others and himself; he has to fly again, to skulk, round Paris, in thickets and stone-quarries. And so at the Village of Clamars, one bleared May morning, there enters a Figure, ragged, rough-bearded, hunger-stricken; asks breakfast in the tavern there. Suspect, by the look of him! "Servant out of place, sayest thou?" Committee-President of Forty-Sous finds a Latin Horace on him: "Art thou not one of those Ci-devants that were wont to keep servants? Suspect!" He is haled forthwith, breakfast unfinished, towards Bourg-la-Reine, on foot: he faints with exhaustion; is set on a peasant's horse; is flung into his damp prison-cell: on the morrow, recollecting him, you enter; Condorcet lies dead on the floor. They die fast, and disappear: the Notabilities of France disappear, one after one, like lights in a Theatre, which you are snuffing out.