## 11 factorizations at 552 digits

Expand Messages
• Yet another weekend record update! :) Don t worry though, things will slow down soon! This is a string of 11 factorizations at 552 digits. All primes were
Message 1 of 5 , Dec 6, 2009
Yet another weekend record update! :) Don't worry though, things will slow down soon!

This is a string of 11 factorizations at 552 digits.

All primes were verified with PARI/GP's isprime function.

Starting N:
------------------------
f(x) = (2*x^3 - 3*x^2 - 5*x + 2)^2 * (4*x^6 - 12*x^5 - 11*x^4 + 38*x^3 + 13*x^2 - 20*x - 6)^2 / 16;
x = 15^26+10620028;
N = f(x)+1;
------------------------

Factorization is as follows:
---------------------------------------------
N-0 = 1061 * 1877 * p545
---------------------------------------------
N-1 = 2^8 * 3^2 * 41^2 * 103^2 * p23^2 * p25^2 * p26^2 * p33^2 * p64^2 * p102^2
---------------------------------------------
N-2 = 5^2 * 13 * 109 * 157 * 179 * 10354103 * p24 * p31 * p57 * p72 * p110 * p244
---------------------------------------------
N-3 = 2 * 7 * 199 * 383 * 22769 * 1981631 * 228901271 * 7062362423 * 9533727384721 * 906067834230707143 * 64730151242356234799 * p39 * p39 * p51 * p66 * p72 * p92 * p110
---------------------------------------------
N-4 = 3 * 457 * 6781 * 13042499 * 215026223 * 2776982627 * 945861378949 * 25483746753600361 * p25 * p28 * p50 * p91 * p133 * p167
---------------------------------------------
N-5 = 2^2 * 17 * 1613 * 3607 * 69127 * 424841 * 425109049 * 6325447759 * 10312284591953317 * 746927965061759029 * p23 * p36 * p40 * p51 * p99 * p235
---------------------------------------------
N-6 = 31 * 89 * 181 * 6361 * p542
---------------------------------------------
N-7 = 2 * 3 * 5 * 47 * 331 * 359 * 1291 * 986981 * 2002953749 * p167 * p359
---------------------------------------------
N-8 = 55337 * p547
---------------------------------------------
N-9 = 2^3 * 43487 * 34434429143 * 2671318275315433 * p54 * p126 * p341
---------------------------------------------
N-10 = 3^3 * 7 * 11 * 29 * 797 * 1039 * 1103 * 1427 * 3251 * 3259 * 39103 * 204013 * 535169 * 272886083 * 4121448017 * 21598899661 * 409072561753 * 519537015073 * 858143907144487 * 2678465528135027 * 692182816348603133 * p21 * p27 * p29 * p51 * p133 * p154
---------------------------------------------

As usual, a PARI/GP script is available for more details:
http://immortaltheory.com/cnt/verify_k11_c552.gp

Boundary composites are as follows (includes a p44...)
=====================
N+1 = 2 * 11^2 * 19 * 1884523 * 5051815528104032427515047480883 * 19320078030071947802324076404344843659439811 * c468

N-11 = 2 * 14723 * c547
=====================
For the above, we've run ~2000 ECM curves at 1e6.
• ... I guess there is still a run of 10 at 600 digits in the SNFS = 200 pipeline? David
Message 2 of 5 , Dec 7, 2009
--- In primeform@yahoogroups.com,
"Joe" <joecr@...> wrote:

> Yet another weekend record update! :)
> Don't worry though, things will slow down soon!

I guess there is still a run of 10 at 600 digits
in the SNFS = 200 pipeline?

David
• I figured I should go ahead and invest more time up front to find a longer chain than 10 before going through the SNFS 200. I.e. I m pretty sure either of us
Message 3 of 5 , Dec 7, 2009
I figured I should go ahead and invest more time up front to find a longer chain than 10 before going through the SNFS 200. I.e. I'm pretty sure either of us could find a k=11 candidate at 600 digits pending SNFS factorizations faster than I could finish the SNFS 200s for a k=10. I'm not sure what the right balance is to be the most productive so I left those factorizations on pause for right now.

In fact, I haven't decided yet what next to focus on.

- Joe

>
>
>
> --- In primeform@yahoogroups.com,
> "Joe" <joecr@> wrote:
>
> > Yet another weekend record update! :)
> > Don't worry though, things will slow down soon!
>
> I guess there is still a run of 10 at 600 digits
> in the SNFS = 200 pipeline?
>
> David
>
• ... Congratulations! You people give me some work! The record page is updated again. -- Jens Kruse Andersen
Message 4 of 5 , Dec 7, 2009
Jow wrote:
> Yet another weekend record update! :) Don't worry though, things will slow
> down soon!

Congratulations!
You people give me some work! The record page is updated again.

--
Jens Kruse Andersen
• ... Thanks, Jens, for http://users.cybercity.dk/~dsl522332/math/consecutive_factorizations.htm#length which might help to avoid my exploratory efforts being
Message 5 of 5 , Dec 7, 2009
--- In primeform@yahoogroups.com,
"Jens Kruse Andersen" <jens.k.a@...> wrote:

> The record page is updated again.

Thanks, Jens, for

http://users.cybercity.dk/~dsl522332/math/consecutive_factorizations.htm#length

which might help to avoid my exploratory efforts
being entirely Crumpled by SNFS = 200 (which
I do not intend to undertake: too boring a use
of limited cycles).

David
Your message has been successfully submitted and would be delivered to recipients shortly.