[math-fun] The largest twin-primes known today...
... are: 2996863034895*2^1290000-1 and 2996863034895*2^1290000+1 http://www.primegrid.com/download/twin-1290000.pdf Best, É.
Is anything known about the factorization of that coefficient (other than its divisibility by 5 and 9)? Was it chosen as part of some algorithm that singled out relatively likely candidates? Or was it just stumbled on at random from a massive search? Or maybe one of our factoring experts can factor it? (You know who you are.) —Dan
On Sep 20, 2016, at 3:18 PM, Eric Angelini <Eric.Angelini@kntv.be> wrote:
... are: 2996863034895*2^1290000-1 and 2996863034895*2^1290000+1
P.S. I'm puzzled by this statement about these twin primes at that link: ----- They will enter Chris Caldwell's “The Largest Known Primes Database” (http://primes.utm.edu/primes) ranked 1st for twins, and each entered individually ranked 4180th overall. ----- Why do they have the same ranking overall? Does it not matter that one is bigger than the other? —Dan
On Sep 20, 2016, at 3:35 PM, Dan Asimov <asimov@msri.org> wrote:
Is anything known about the factorization of that coefficient
(other than its divisibility by 5 and 9)?
Was it chosen as part of some algorithm that singled out relatively likely candidates? Or was it just stumbled on at random from a massive search?
Or maybe one of our factoring experts can factor it? (You know who you are.)
—Dan
On Sep 20, 2016, at 3:18 PM, Eric Angelini <Eric.Angelini@kntv.be> wrote:
... are: 2996863034895*2^1290000-1 and 2996863034895*2^1290000+1
Factoris says the coefficient factors to 3^12.5.18583.3583757. On Tue, Sep 20, 2016 at 6:55 PM, Dan Asimov <asimov@msri.org> wrote:
P.S. I'm puzzled by this statement about these twin primes at that link:
----- They will enter Chris Caldwell's “The Largest Known Primes Database” (http://primes.utm.edu/primes) ranked 1st for twins, and each entered individually ranked 4180th overall. -----
Why do they have the same ranking overall? Does it not matter that one is bigger than the other?
—Dan
On Sep 20, 2016, at 3:35 PM, Dan Asimov <asimov@msri.org> wrote:
Is anything known about the factorization of that coefficient
(other than its divisibility by 5 and 9)?
Was it chosen as part of some algorithm that singled out relatively likely candidates? Or was it just stumbled on at random from a massive search?
Or maybe one of our factoring experts can factor it? (You know who you are.)
—Dan
On Sep 20, 2016, at 3:18 PM, Eric Angelini <Eric.Angelini@kntv.be> wrote:
... are: 2996863034895*2^1290000-1 and 2996863034895*2^1290000+1
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Thanks, Allan. I wonder why a coefficient of that form was chosen. There must be some pretty good reason, no? —Dan
On Sep 20, 2016, at 4:05 PM, Allan Wechsler <acwacw@gmail.com> wrote:
Factoris says the coefficient factors to 3^12.5.18583.3583757.
On Tue, Sep 20, 2016 at 6:55 PM, Dan Asimov <asimov@msri.org> wrote:
P.S. I'm puzzled by this statement about these twin primes at that link:
----- They will enter Chris Caldwell's “The Largest Known Primes Database” (http://primes.utm.edu/primes) ranked 1st for twins, and each entered individually ranked 4180th overall. -----
Why do they have the same ranking overall? Does it not matter that one is bigger than the other?
—Dan
On Sep 20, 2016, at 3:35 PM, Dan Asimov <asimov@msri.org> wrote:
Is anything known about the factorization of that coefficient
(other than its divisibility by 5 and 9)?
Was it chosen as part of some algorithm that singled out relatively likely candidates? Or was it just stumbled on at random from a massive search?
Or maybe one of our factoring experts can factor it? (You know who you are.)
—Dan
On Sep 20, 2016, at 3:18 PM, Eric Angelini <Eric.Angelini@kntv.be> wrote:
... are: 2996863034895*2^1290000-1 and 2996863034895*2^1290000+1
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Arrgh. I see I'm having trouble reading simple English: *each* *entered* *individually* explains my confusion. As I said: Arrgh. —Dan
On Sep 20, 2016, at 3:55 PM, Dan Asimov <asimov@msri.org> wrote:
-----
. . . each entered individually ranked 4180th overall.
Why do they have the same ranking overall? Does it not matter that one is bigger than the other?
participants (3)
-
Allan Wechsler -
Dan Asimov -
Eric Angelini