6+ table

[garo]

Size	Base	Index	Mod	Diff	Ratio	
261	6	419	+	326	0.798	
246	6	421	+	327.6	0.749	
331	6	431	+	335.3	0.985	
258	6	436	+	339.2	0.758	
270	6	439	+	341.6	0.788	
282	6	443	+	344.7	0.816	
289	6	448	+	298.8	0.965	/7/resvd
283	6	449	+	349.3	0.807	
247	6	454	+	353.2	0.698	
344	6	457	+	355.6	0.965	
336	6	458	+	356.3	0.941	
327	6	463	+	360.2	0.906	
311	6	464	+	361	0.859	
320	6	466	+	362.6	0.881	
312	6	472	+	367.2	0.848	
281	6	473	+	334.6	0.838	/11q
338	6	478	+	371.9	0.907	
309	6	479	+	372.7	0.827	
337	6	481	+	345.4	0.973	/13
268	6	482	+	375	0.713	
307	6	484	+	342.3	0.895	/11q
282	6	488	+	379.7	0.741	
330	6	493	+	383.6	0.858	
255	6	494	+	354.8	0.8	/13
315	6	496	+	385.9	0.814	
258	6	497	+	331.4	0.776	/7
294	6	499	+	388.2	0.75

[jyb]

GMP-ECM 6.0.1 curves run on 6,762M (with default B2):
4362 curves with B1 = 11e6
6791 curves with B1 = 43e6
15504 curves with B1 = 11e7

-Jon

[geoff]

6,363+ C172 = P75.P98
P75=103373476033477388263515282957106895317857131511194597652434632687520479231

This was done with ggnfs-0.77.1 using polynomial 36x^6-6x^3+1, 28 bit large primes, and algebraic/rational factor base limits of 14.8/16 million.

[geoff]

6,287+ C154 = P66.P88
P66=247859037729470996906245243451923112548845447499779115951590660463

This was by SNFS (difficulty 191.4) with ggnfs-0.77.1, using polynomial x^6-x^5+x^4-x^3+x^2-x+1, 28 bit large primes, and algebraic/rational factor base limits of 14.7/20 million.

Sieving took 66 GHz days on a mix of P2,P3,P4 CPUs, linear algebra took 10 GHz days on a P4, peak RAM usage was 714 MB.

[geoff]

6,798L C140 = P57 * P84
P57 = 286227504202337752215096844369178117421662207554962805489

This was by GNFS with ggnfs CVS 20060310 using 28 bit large primes and algebraic/rational factor base limits of 14.1/14.0 million.

Polynomial search took 9 GHz days on a P4/Celeron, sieving took 93 GHz days on a mix of P2,P3,P4 CPUs, linear algebra (on the third attempt) took 11 GHz days on a P4. Peak RAM usage was about 850 MB.

[smh]

The factorization of 6^369+1

N=1995318523583569410536518710238825992069432091418126270747301312022729565418312904399527685768670754705838744041545211857263269211105325133582097428175392915125238452242062431167 ( 178 digits)
SNFS difficulty: 191 digits.
Divisors found:
r1=13962920965423422985070859383439633233088296131740062300197159 (pp62)
r2=142901225934358910616458334546032475881108357631878872140161426564856550164076857572859982163043154061736815224575913 (pp117)

[xilman]

Originally Posted by smh

The factorization of 6^369+1

N=1995318523583569410536518710238825992069432091418126270747301312022729565418312904399527685768670754705838744041545211857263269211105325133582097428175392915125238452242062431167 ( 178 digits)
SNFS difficulty: 191 digits.
Divisors found:
r1=13962920965423422985070859383439633233088296131740062300197159 (pp62)
r2=142901225934358910616458334546032475881108357631878872140161426564856550164076857572859982163043154061736815224575913 (pp117)

Nice one.

Sam's news letter arrived here this morning. Not sure whether you've received yours yet.


Paul

[smh]

Originally Posted by xilman

Sam's news letter arrived here this morning. Not sure whether you've received yours yet.

Only a confirmation that he recieved the factors.
I guess i have to ask prof. Wagstaff to be included in this mailing list?

[bdodson]

Originally Posted by garo

Base	Index	Size	11M(45digits)	43M(50digits)	110M(55digits)	260M(60digits)	Decimal
...
6	337+	C156	0(2.63512)	2160(0.477957)	0(0.0754361) 300(0.0068697)	
607055099444498921847583147982450809557514004451282871917948174791099265283291964431544302627498111551020109672026017537034605137651109768044489243175210279
...

Not sure that I can give entirely satisfactory reasons, but the Opterons
with first limit 110M (p55-optimal) are running circles around the xp's
and the P3's (and another 80-some xeons that went idle), all with
first limit 43M (p50-optimal). Score: 5-to-2. My intended reason was
that c155-c169's tested to p50 were more likely to factor than the
c234-c299 (as well as some time in c3xx), even though the latter were
only tested to p45. With explanation that too many of the c234-c366's
with factors under p45 removed had (on average) few factors in ecm
range (like lots with smallest factor above p100, say). The first step
limits oughtn't to make that much difference, as the factors being found
are well within range of the smaller limits, given a larger number of
curves. I'm fairly certain that the xp's are spending considerably more
"work units" (without actually checking how these are actually defined);
and with the addition on the xeons there's now a fairly substantial effort
on the c155-c169's of difficulty under 220, that hasn't found anything
at all (this year). Perhaps that's since smaller difficulty numbers had
more ecm (from other users?), or the previous runs used smaller limits,
so were less likely to miss p46-p54 factors (smaller standard deviation?).

Anyway, here's the new one,

p53=84382257093351217403808536729720911956398743537658819

with snfs difficulty 262.24, way harder than the 156-digit gnfs. -Bruce

[bdodson]

Originally Posted by garo

Base    Index    Size    11M(45digits)    43M(50digits)    110M(55digits)    260M(60digits)    Decimal
...
6    365+    C182    0(2.09174)    1500(0.38003)    590(0.0622008)    0(0.00529647)
18277199064023868716464418337366764898392423901374182657841980711016975079192366008607903315073044637550970940888219527035615248207222941096199986090387235389044400550718035078208621
...

Another Opteron factor from the c170-c189's of difficulty 220 and up. One
of the good points about this range is that any factor is likely to be useful.
In this case, even the relatively low snfs difficulty 227 is way-harder than
the cofactor:

p60 = 254856004505238557834753259615355816338030694854500477132141

from c182, leaving a c122. I haven't heard yet from the usual suspects,
but anyone considering polishing off the cofactor (please!) should make
sure that they have a reservation with Sam before starting. -Bruce

PS - this was from the 2nd Opteron pass, which has since finished on
the c182/c122. So it's at 1.66*t50, ready for gnfs (presumably). [2*t50, actually]

[akruppa]

Your p60 isn't prime,

54856004505238557834753259615355816338030694854500477132141 = 3 * 32827965463229429509624429 * 557004815164707788478198263318443

nor do any of the two larger prime factors divide a Cunningham number.

Cut-and-paste error?

Alex