I think Allan means 3^2, not 3^12. This would have been an extremely easy factorization even for Lehmer's optical contraption <https://en.wikipedia.org/wiki/Lehmer_sieve>. Or Macsyma back when it trial-divided by consecutive odd numbers. Which is pretty much like GCDing with their product, now that we can store big numbers. I just wrote a tiny (and very untested) recursive program in a similar vein: In[832]:= Clear[dumfac]; dumfac@1 = {}; dumfac[n_Integer] := (dumfac@n = {n}; dumfac@n = Join[dumfac[#], dumfac[n/#]] &@ GCD[n, Binomial[#, Floor[#/2]] &@Floor[Sqrt[n]]]) In[833]:= dumfac[2996863034895] // tim During evaluation of In[833]:= 0.188517 sec, 5 Out[833]= {5, 3, 3, 18583, 3583757} In[834]:= PrimeQ /@ % Out[834]= {True, True, True, True, True} --rwg On 2016-09-20 16:05, Allan Wechsler 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