We report the factorization of the Bernoulli numerator
B_240 using CADO-NFS 1.1. The 186-digit number we factored is
658668195017872453574645920506670150851515186543024450323395963158
924251877705747032509465107947879360925185409205270190334183597874
188845304483162876301650530183414130668463501455159621
When it was split, this number was the second largest number ever
factored by CADO-NFS.
Its factors are
P71 =
76636706942918875949500173248943195134501625321082166469500302265643349
and
P115 =
859468290447900657605137245690284560697193444824839160343932897776
0426480832015361264099417520110721293192996372529
Shi Bai used a special developmental version of CADO-NFS to find the
good polynomials
f(x) = 9187200 * x^5
- 892937430204032 * x^4
+ 83718006762578350746290 * x^3
- 14624038229659491461981075131151 * x^2
- 473212311680074476313019654976963486078 * x
+ 5856872011138406855250364104913595127959346075
and
g(x) = 127503258496759399 * x
- 590332515065734561034626243485130174
with the properties:
skew: 57294848.000
# lognorm: 60.63, alpha: -8.76 (proj: -2.41), E: 51.87, nr: 3
# MurphyE(Bf=10000000,Bg=5000000,area=1.00e+16)=3.11e-14
I used the following parameters for lattice sieving of special q
between 1e7 and 166e7.
rlim=40000000
alim=80000000
I=14 (I=15 would have been better.)
lpbr=32
lpba=32
mfbr=64
mfba=96
rlambda=2.1
alambda=3.2
The sieving took one week in November, 2012,
on Purdue's Condor system using about 10K cores.
This produced 48GB of raw relations (compressed).
Before Pass 1 of purge, there were 380589160 prime ideals
and 362182783 relations. At the end of Pass 1,
nrel=242566960, nprimes=197856246; excess=44710714.
At the end of Pass 2,
nrel=101744610, nprimes=101744450; excess=160.
In purgelog, the weight was 2235745261 and weight*nrows=2.27e+17.
After replay, the small_nrows was 32170335.
In bwc, krylov went up to N=1006000 and mksol went up to N=502662.
The linear algebra started in November, 2012, and ran on one
node (16 cores) of two 8-core Intel Xeon-E5 processors. See
www.rcac.purdue.edu/userinfo/resources/carter/
The linear algebra finished April 2, 2013.
The factors were found later that day.
The first dependency aborted due to not enough memory:
maximal polynomial bit-size = 18446744072631487173
Using p=127 for lifting
target size=10145709239947317944
GNU MP: Cannot reallocate memory (old_size=8 new_size=2415919144)
The second dependency factored the number.
The complete factorization of this Bernoulli numerator is:
B_240 = C291 = 421.249107671.26230095767160160157.
.594882757933212956744777900034818887.
.196861064367657026999864250178278857143.
.76636706942918875949500173248943195134501625321082166469500302265643349.P115
P115 =
8594682904479006576051372456902845606971934448248391603439328977760426480832
015361264099417520110721293192996372529
Sam Wagstaff