Re: [PrimeNumbers] Re: Prime chains x-->Ax+B [puzzle 2]
- Hello David,
At 09:43 AM 3/01/2011, djbroadhurst wrote:
>--- In email@example.com, Kevin Acres <research@...> wrote:Thanks for that. It will give me some idea of what to hope for at least.
> > after now having found 17 15/16 chains, should
> > I reasonably be expecting a 16/16 some time soon?
>Suppose that you guessed a 1/9 chance. Then the odds
>of /not/ getting a result after 17 tries are
>exp(-17/9) =~ 15%
Right now I'm trawling shallow waters again. This gives me faster
processing and a greater 15/16 density. Over the next couple of days
I'm going to take b up to just less than 2^31 with x < 51561510. I
expect this to give an extra 6 or so 15/16 chains on top of the 18 I have now.
The current state of my search is:
0 < b < 506306000, 0 < x < 511020510 -> completed
506306000 < b < 1000479680, 0 < x < 51561510 -> completed
1000479680 < b < 1600328930, 0 < x < 51561510 -> 50% complete (~17
hours to go)
1600328930 < b < 2147085140, 0 < x < 51561510 -> not yet started (~32 hours)
For completeness, my 18th 15/16 is:
[18*x + 1220760325, [38738527, 15]]
- --- In firstname.lastname@example.org,
Kevin Acres <research@...> wrote:
> x=a*x+b either is a square or has a square as a major factor.Suppose that we want to start with a square and get a square.
Then we must solve the Diophantine equation
y^2 = a*x^2 + b
For any pair (a,b), Dario will tell us all the solutions: