RSA190 (not completed yet)


"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.


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
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)


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