# RSA190 (not completed yet)

### Comments

"the number was factored by I.Popovyan from MSU, Russia and A. Timofeev from CWI, Netherlands and took a few months of a pure computer time on various parallel systems in both MSU and CWI" (mersenneforum).
The polynomial they used is (information generated by CADO-NFS),

c5: 40208599020

c4: -1373979915646426

c3: -18783091380980602091391

c2: 32414999912320727344430346523

c1: -375830488267489810578184841744243639

c0: 348578818479643113591848726218653819076813

Y1: 127570152207571988302487

Y0: -543540225411856459303967064165519554

# lognorm 59.40, alpha -5.64, 1 rroots

# Murphy's E(Bf=10000000,Bg=5000000,area=1.00e+16)=1.55e-14 (CADO-NFS)

This polynomial seems to be the best one along its neighbour rotation space (10000x50000000000) by rootsieve in CADO-NFS.

### Polynomial

The polynomial was generated using the (very) large prime variant of Thorsten Kleinjung 's algorithm. The root sieve was done in the following way. First, rotates many raw polynomials along the best sublattice and treat them as raw polynomials, then run msieve on these rotated polynomials. However, it seems (countering to my initial purpose) that the only effect of doing the rotation is to enlarge the size of the polynomial. Now, CADO-NFS might be able to do this directly. Finally, several sieve tests are done to pick the following polynomial.
n: 1907556405060696491061450432646028861081179759533

1844606479756223189150255871841757540549761551215932

9349226046415263009323850924660320741712472612158085

8185985938946945490481721756401423481

c5: 255190140

c4: -47260029758132866

c3: 11100977719061907146275874

c2: 199076980463854285552426407486731

c1: -5248708483538855234690491711962684053766

c0: 5447894568502905764476664798517077173925915847

Y1: 2642639550249635903

Y0: -1495280603333333570159597505117010240

# lognorm 63.72, alpha -8.81, 3 rroots

# Murphy's E(Bf=10000000,Bg=5000000,area=1.00e+16)=1.30e-14 (CADO-NFS)

# norm 8.395467e-19 alpha -8.805648 e 1.465e-14 rroots 3 (msieve)

### Sieving

Lattice sieve was done in lasieve. Until 8 Nov, 322598211 unique relations were collected. The msieve gave a matrix of size 45Mx45M. Some more sieving will be done until the taking-down of the cluster next week.
rlim: 100000000

alim: 200000000

lpbr: 32

lpba: 32

mfbr: 64

mfba: 96

rlambda: 2.4

alambda: 3.4

### Filtering and linear algebra