[math-fun] Largest ever proof
http://www.nature.com/news/two-hundred-terabyte-maths-proof-is-largest-ever-... à+ É. Catapulté de mon aPhone
The Lucas-Lehmer test that M74207281 is prime requires 74M steps. Writing down the remainders of the X2-2 (mod P) iteration, at 22M digits each, would take 1.6Q characters. If we included the arithmetic to confirm each squaring step, another factor of 22M, we have 35 sextillion characters. We could reduce this a lot with Karatsuba or FFT multiplication, but we're still at 1.6Q * log2(74M) ~= 40 quadrillion characters. Is this any different from the 200T problem? Rich -------------- Quoting Eric Angelini <Eric.Angelini@kntv.be>:
http://www.nature.com/news/two-hundred-terabyte-maths-proof-is-largest-ever-...
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I agree with Rich here; I'm not sure I see the problem. Suppose somebody conjectures that some predicate P is true of all positive integers, and manages to prove P(n) for n > 6 x 10^54. Then somebody betters the bound to n > 2 x 10^41. Then a third person throws half the Amazon Cloud at the problem for six months and announces that they have checked P(n) for all n up to that bound. Is the conjecture not proven yet? What would it take? On Fri, May 27, 2016 at 6:29 PM, <rcs@xmission.com> wrote:
The Lucas-Lehmer test that M74207281 is prime requires 74M steps. Writing down the remainders of the X2-2 (mod P) iteration, at 22M digits each, would take 1.6Q characters. If we included the arithmetic to confirm each squaring step, another factor of 22M, we have 35 sextillion characters. We could reduce this a lot with Karatsuba or FFT multiplication, but we're still at 1.6Q * log2(74M) ~= 40 quadrillion characters.
Is this any different from the 200T problem?
Rich
--------------
Quoting Eric Angelini <Eric.Angelini@kntv.be>:
http://www.nature.com/news/two-hundred-terabyte-maths-proof-is-largest-ever-...
à+ É. Catapulté de mon aPhone
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Provable is a rigorous concept (from a given set of axioms). Proven is not. How do you know that the rules of proof have been followed? How do you know that the people or computer program telling you have didn't commit some error. Etc. —Dan
On May 27, 2016, at 7:57 PM, Allan Wechsler <acwacw@gmail.com> wrote:
I agree with Rich here; I'm not sure I see the problem. Suppose somebody conjectures that some predicate P is true of all positive integers, and manages to prove P(n) for n > 6 x 10^54. Then somebody betters the bound to n > 2 x 10^41. Then a third person throws half the Amazon Cloud at the problem for six months and announces that they have checked P(n) for all n up to that bound. Is the conjecture not proven yet? What would it take?
participants (4)
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Allan Wechsler -
Dan Asimov -
Eric Angelini -
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