## 9 consecutive factorizations at 804 digits

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• I d like to announce a string of 9 consecutive factorizations at 804 digits! This required two SNFS 202 difficulty factorizations.
Message 1 of 5 , Dec 6, 2009
I'd like to announce a string of 9 consecutive factorizations at 804 digits!

This required two SNFS 202 difficulty factorizations.

http://immortaltheory.com/cnt/c804.html

All primes were verified with PARI/GP isprime.

N starts at...
---------------------------------------------
x=2310*(10^30+40790547)+5;
t1=5*x*x*x-x*x-x-1;
t2=(t1*(5*t1+9)/2-31)^2;
N=(t2-23*23)*(t2-24*24)/55440;
---------------------------------------------

And factorizations are as follows...
---------------------------------------------
N-0 = 2^2 * 11^2 * 29 * 73 * 643 * 727 * 3547 * 86851 * 915283 * 4719726079 * 14266216717 * 19750153781 * 172788128959 * 17346192250609 * 365172908112440801 * 11349953878687101971 * p22 * p29 * p57 * p99 * p101 * p112 * p126 * p143
---------------------------------------------
N-1 = 3 * p803
---------------------------------------------
N-2 = 2 * 5 * p803
---------------------------------------------
N-3 = 7 * 17 * 37 * 157 * 283 * 317 * 419 * 691 * 1433 * 1901 * 1913 * 6689 * 2439953 * 2653993787 * 3079307041 * 6361306879 * 1848987653587 * 147279592197387043 * p25 * p45 * p52 * p58 * p63 * p64 * p80 * p142 * p185
---------------------------------------------
N-4 = 2^11 * 3 * 13 * 19 * 23^2 * 43 * 47 * 53 * 71 * 79 * 103 * 113 * 131 * 313 * 389 * 619 * 1093 * 1579 * 7451 * 13309 * 33569 * 76757 * 92627 * 1319261 * 1114238843 * 18290398183 * 489625035961 * 1270641752531 * 52875541480393 * 3354903562911899 * 52004118381270427 * 63033107717874313 * 717795020292627461 * p26 * p28 * p33 * p35 * p37 * p39 * p53 * p57 * p60 * p68 * p88 * p95
---------------------------------------------
N-5 = 2423 * 101557755913 * 266403633889 * p778
---------------------------------------------
N-6 = 2 * 61 * 2011 * 10601 * 444546250219 * p783
---------------------------------------------
N-7 = 3^3 * 5 * 331 * p799
---------------------------------------------
N-8 = 2^2 * 4261 * 75337 * 110917 * 574283 * 15755933 * 255946099 * 166880080123 * p757
---------------------------------------------

Boundary composites are as follows...
==============
N+1 = 599 * 919 * 3779 * 42649 * 16228241 * 61486981526111 * c769
N-9 = 41 * 535101467 * c793
==============

For the above, we've run ~2000 ECM curves at 1e6 and ~500 at 3e6 with no further factors.
• ... Congratulations! It is also record for 8 numbers. This means all records from 8 to 12 numbers were set on the same day. The record page is updated. The
Message 2 of 5 , Dec 6, 2009
Joe wrote:
> I'd like to announce a string of 9 consecutive factorizations at 804 digits!
>
> This required two SNFS 202 difficulty factorizations.
>
> http://immortaltheory.com/cnt/c804.html

Congratulations!
It is also record for 8 numbers. This means all records from
8 to 12 numbers were set on the same day.
The record page is updated. The tables now link to the
factorizations. The new record factorization is here:
http://users.cybercity.dk/~dsl522332/math/consecutive_factorizations.htm#k9_804

--
Jens Kruse Andersen
• ... Capital work! How pleasant that all the records from k = 8 to k = 12 arrived on the same day. David
Message 3 of 5 , Dec 6, 2009
--- In primeform@yahoogroups.com,
"Joe" <joecr@...> wrote:

> I'd like to announce a string of 9 consecutive
> factorizations at 804 digits!

Capital work! How pleasant that all the records
from k = 8 to k = 12 arrived on the same day.

David
• I ve had a look at how the sextics broke. Recall that my Ansatz reduced 12 sextics to 6. Joe neatly got rid of one more, algebraically, as remarked in
Message 4 of 5 , Dec 6, 2009
I've had a look at how the sextics broke. Recall that my
Ansatz reduced 12 sextics to 6. Joe neatly got rid of one
more, algebraically, as remarked in
http://tech.groups.yahoo.com/group/primeform/message/9822?var=0
Only two of the remaining 5 sextics needed SNFS, in this
impressive record. Each of other 3 has a second largest prime
factor with less than 30 digits, which was quite good luck.

Might you please give some details, Joe, of the total number
of GHz-hours to crack a target with SNFS difficulty of ~204.
That difficulty lies considerably beyond my own experience.

David
• The c169 was ~11 days on a Q8200 quad core (~1000 hrs split up by 4 threads. The c199 was ~13 days (~1300/4 hrs). This was in the ballpark of my original SWAG
Message 5 of 5 , Dec 6, 2009
The c169 was ~11 days on a Q8200 quad core (~1000 hrs split up by 4 threads. The c199 was ~13 days (~1300/4 hrs). This was in the ballpark of my original SWAG estimate of ~10 days.

I used rlim/alim at 20,000,000 and lpbx/mfbx at 28/56 after consulting MersenneForum to sanity check my original planned parameters:

- Joe

>
>
>
> I've had a look at how the sextics broke. Recall that my
> Ansatz reduced 12 sextics to 6. Joe neatly got rid of one
> more, algebraically, as remarked in
> http://tech.groups.yahoo.com/group/primeform/message/9822?var=0
> Only two of the remaining 5 sextics needed SNFS, in this
> impressive record. Each of other 3 has a second largest prime
> factor with less than 30 digits, which was quite good luck.
>
> Might you please give some details, Joe, of the total number
> of GHz-hours to crack a target with SNFS difficulty of ~204.
> That difficulty lies considerably beyond my own experience.
>
> David
>
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