Sieving 10^462+1

[xilman]

Originally Posted by R.D. Silverman

The Cunninghams are all repunits. Just in different bases.

All composite numbers are repunits. Just in different bases.

[Mini-Geek]

Originally Posted by xilman

All composite numbers are repunits. Just in different bases.

Not just composite numbers. n=11_n-1

[xilman]

Originally Posted by Mini-Geek

Not just composite numbers. n=11_n-1

The discussion was in the context of factoring. Factoring primes is rather trivial.

My original intent was to say "all numbers", carefully being sloppy in identifying "numbers" with the rings Z or N , but the statement is no longer true for abs(n) < 3. Rather than unduly complicating matters, I chose to restrict my statement to composite numbers.


Paul

[R.D. Silverman]

Originally Posted by xilman

All composite numbers are repunits. Just in different bases.

Representing N in base N isn't very interesting...........

[axn]

Originally Posted by R.D. Silverman

Representing N in base N isn't very interesting...........

Aha! N = 11(base N-1)! There. That _must_ be interesting

[wreck]

Originally Posted by juno1369

I am not going to factor both these numbers because my laptop keeps restarting automatically and sometimes shutting down itself when I run polyselect. I leave these two numbers for someone else to factor.

If the polynomial is the only problem you meet, you can have a try to the snfs.
The easiest one is 10^405-1, and its poly is

n: 3517412599793609476455168711048853577877869285903909511672490597786154396101045678221196660571883869013967834755445386746946314375802833469406378013185319317311967782209292276167648593890678001
# 10^405-1, difficulty: 216.00, skewness: 1.00, alpha: 1.68
# cost: 5.52232e+17, est. time: 262.97 GHz days (not accurate yet!)
skew: 1.000
c4: 1
c3: -1
c2: -4
c1: 4
c0: 1
Y1: -1000000000000000000000000000
Y0: 1000000000000000000000000000000000000000000000000000001
m: 3516412599793609476455168711049853577877869285903909511672490597786154396101045678220196660571883869013967834756445386746946314375802833468406378013185319317311967783209292276167648593890678002
type: snfs

This number would take about 15000 CPU hours.

After nearly 4 months' effort, we just brought down this c159 and split it into two pieces.

c159=p79*p81

with

p79=3925277248426748966984537733816767395325307476622633188305245093834818012069881

p81=130547462818138630777456508666491939964821812774903307594092374520935816757936709

These primes are certified with Primo.

We used the polynomial that wreck mentioned. This number took ~62M relations to factor. It produced a 7.4M*7.4M matrix and took 168h on a P7450 to do linear algebra (with 2 threads).

This is a joint effort by myself, pchu, wreck and wpolly.

And now finally I can turn back to some other volunteer computing project...

fwjmath