M334105069 has a factor: 42497896751699756959
k=127199197782=2*3^2*401*569*30971
^My first 100m+ digit with a factor

Personal Record ...
 

... and appears to be the largest in this thread-

M56226553 has a factor: 134624114590567994209661373751147664039

It is prime, and k = 1197157814303217149108014622123
= 7 × 5717 × 26371 × 29101 × 70051 × 104677 × 5316001

126.662 bits

Found the following factor doing P-1 with bounds of B1=105000, B2=2126250

M3121633 has a factor: 131414729529446443905414328694253075246015919

which is composite 16493495072423946793 x 7967670221041466332789783

It's been a while...
 

[SIZE=2]M[/SIZE][SIZE=2]6950959 has a factor: [/SIZE][SIZE=2]132059386138894835524513023632401 (107 bits)

k = 2^3 * 3^3 * 5^2 * 7^4 * 13 * 52721 * 246187 * 4342267

P-1, B1=440000, B2=13530000
[/SIZE]

Found this baby today... really smooth, isn't it? And it is not in the low 70bit area.

M52992127 has a factor: 60514492674650918971620097 (85.64 Bits; k = 570976257233937024 = 2[SUP]7[/SUP] * 3[SUP]4[/SUP] * 19 * 23[SUP]3[/SUP] * 29 * 37 * 53 * 59 * 71)

P-1 found a factor in stage #2, B1=680000, B2=20230000.
M56909563 has a factor: 84773527927083202608069060159088670986010852161

Composite:

334280937484386845377
k= 2^5 * 3 * 1823 * 16781797

and

253599647545091299492747393
k= 2^6 * 3 * 7 * 31 * 101 * 575173 * 920561

ECM found a factor in curve #113, stage #2
Sigma=2903048005667313, B1=250000, B2=25000000.
M200341 has a factor: 9262749031172873562732662148096079
k = 3 ^ 3 x 7 x 17 x 575668759 x 12498464974205537

This is the first "triple" I have seen
 

[FONT=Arial]M602249941 has a factor: 86439049638640106399[/FONT]
[FONT=Arial]M602249941 has a factor: 77482243219676340503[/FONT]
[FONT=Arial]M602249941 has a factor: 22781228486416840393[/FONT]
[FONT=Arial]found 3 factor(s) for M602249941 from 2^64 to 2^67 [mfaktc 0.17-Win barrett79_mul32][/FONT]

[FONT=Arial]This is the first time I have found three factors.[/FONT]

[FONT=Arial]Chuck[/FONT]

M3305873 has a factor: 6999440290894365093551488666249 (103 bits)
k = 2^2 × 3^2 × 13^2 × 211 × 18301 × 28183 × 37139 × 43051
P-1 found a factor in stage #1, B1=55000.

M1826807 has a factor: 183484724146379149891934120369 (98 bits)
k=2^3 × 19^2 × 431 × 797 × 22637 × 35129 × 63659
P-1 found a factor in stage #2, B1=45000, B2=607500

[FONT=Calibri][SIZE=3][Oct 8 08:33] P-1 found a factor in stage #2, B1=650000, B2=18850000.[/SIZE][/FONT]
[FONT=Calibri][SIZE=3][Oct 8 08:33] M53918593 has a factor: 379036136699415863361754869721057 (109 bits)[/SIZE][/FONT]

[FONT=Calibri][SIZE=3]I don't know how you folks find the value of k.[/SIZE][/FONT]

[FONT=Calibri][SIZE=3]Chuck[/SIZE][/FONT]

[QUOTE=Chuck;273773]I don't know how you folks find the value of k.[/QUOTE]

F = 2kp+1
F = 379036136699415863361754869721057
p = 53918593

k = (F - 1) / (2p) = 3514892689238161902349296

[QUOTE=TheJudger;273774]F = 2kp+1
F = 379036136699415863361754869721057
p = 53918593

k = (F - 1) / (2p) = 3514892689238161902349296[/QUOTE]

But everyone else shows it as factors; how do they do that?

Chuck

[QUOTE=Chuck;273776]But everyone else shows it as factors; how do they do that?

Chuck[/QUOTE]

[URL="http://factordb.com/index.php?query=3514892689238161902349296"]They just factor it.[/URL]

[QUOTE=lorgix;273780][URL="http://factordb.com/index.php?query=3514892689238161902349296"]They just factor it.[/URL][/QUOTE]

[URL="http://factordb.com/index.php?id=2"][COLOR=#000000]2^4[/COLOR][/URL] · [URL="http://factordb.com/index.php?id=3"][COLOR=#000000]3[/COLOR][/URL] · [URL="http://factordb.com/index.php?id=293"][COLOR=#000000]293[/COLOR][/URL] · [URL="http://factordb.com/index.php?id=919"][COLOR=#000000]919[/COLOR][/URL] · [URL="http://factordb.com/index.php?id=188563"][COLOR=#000000]188563[/COLOR][/URL] · [URL="http://factordb.com/index.php?id=409529"][COLOR=#000000]409529[/COLOR][/URL] · [URL="http://factordb.com/index.php?id=3521653"][COLOR=#000000]3521653[/COLOR][/URL]

Great; I didn't know about that link.

Chuck

[QUOTE=Chuck;273782][URL="http://factordb.com/index.php?id=2"][COLOR=#000000]2^4[/COLOR][/URL] · [URL="http://factordb.com/index.php?id=3"][COLOR=#000000]3[/COLOR][/URL] · [URL="http://factordb.com/index.php?id=293"][COLOR=#000000]293[/COLOR][/URL] · [URL="http://factordb.com/index.php?id=919"][COLOR=#000000]919[/COLOR][/URL] · [URL="http://factordb.com/index.php?id=188563"][COLOR=#000000]188563[/COLOR][/URL] · [URL="http://factordb.com/index.php?id=409529"][COLOR=#000000]409529[/COLOR][/URL] · [URL="http://factordb.com/index.php?id=3521653"][COLOR=#000000]3521653[/COLOR][/URL]

Great; I didn't know about that link.

Chuck[/QUOTE]

It is a great resource.

You may also want to check out [URL="http://www.mersenneforum.org/showthread.php?t=10871"]YAFU[/URL] (long thread), a simple program that lets you factor numbers that Prime95 isn't suited for.

[QUOTE=lorgix;273784]It is a great resource.

You may also want to check out [URL="http://www.mersenneforum.org/showthread.php?t=10871"]YAFU[/URL] (long thread), a simple program that lets you factor numbers that Prime95 isn't suited for.[/QUOTE]

Or [url=http://pari.math.u-bordeaux.fr/]PARI/GP[/url]. There are lots of tools for factoring small numbers.

[QUOTE=Mr. P-1;273797]Or [url=http://pari.math.u-bordeaux.fr/]PARI/GP[/url]. There are lots of tools for factoring small numbers.[/QUOTE]
I like Dario's applet: [url]http://www.alpertron.com.ar/ECM.HTM[/url]

[QUOTE=Mr. P-1;273797]Or [URL="http://pari.math.u-bordeaux.fr/"]PARI/GP[/URL]. There are lots of tools for factoring small numbers.[/QUOTE]

I think YAFU requires less knowledge to get going. At least that was my reasoning.

[QUOTE=Uncwilly;273799]I like Dario's applet: [URL]http://www.alpertron.com.ar/ECM.HTM[/URL][/QUOTE]

Sure, but it "only" uses ECM.

Factoris
 

I'm fond of [URL="http://wims.unice.fr/wims/wims.cgi?cmd=new&module=tool/algebra/factor.en"]Factoris[/URL]

[QUOTE=lorgix;273800]I think YAFU requires less knowledge to get going. At least that was my reasoning.[/QUOTE]

Not really. The same commard - factor(younumber) - works in both utilities.

The two programs have different strengths and purposes. Yafu is a multi-algorithm factorisation utility. PARI/GP is a general purpose computer algebra engine. Neither application breaks sweat at this task.

[QUOTE=cheesehead;273823]I'm fond of [URL="http://wims.unice.fr/wims/wims.cgi?cmd=new&module=tool/algebra/factor.en"]Factoris[/URL][/QUOTE]

When you have a powerful computer sitting on your own desk, why would you want to use someone else's?

[QUOTE=Mr. P-1;273860]When you have a powerful computer sitting on your own desk, why would you want to use someone else's?[/QUOTE]Inertia of not having obtained one of those utilities?

General acquisitional desire?

Habit?

M3870563 has a factor: 36174716570195216701279948305449 (105 bits)
k= 2^2 × 31 × 37 × 199 × 257 × 479 × 7727 × 52237 × 103007
P-1 found a factor in stage #2, B1=70000, B2=1137500

Nothing special
 

Just eliminated my first candidate by the extended trial factoring limits - nothing special but P-1 would have failed:
[CODE]59,382,511 has a factor 2314158515565593764471.
k = 3^1 * 5^1 * 13^3 * 591,266,447[/CODE]factored via [URL]http://www.brennen.net/primes/FactorApplet.html[/URL]

M3814501 has a factor: 632247211624200804682536146686273 (109 bits)
k = 2^5 × 3^2 × 13 × 29 × 397 × 4327 × 5531 × 29363 × 2735923
P-1 found a factor in stage #2, B1=65000, B2=1121250.

M332245103 has a factor: 36412218749212999860737
found 1 factor(s) for M332245103 from 2^74 to 2^75

My first factor :big grin:

I use Factor5 to find my factors:

M77345993 has a factor: 1010293360567
No other factors between 2[sup]26[/sup] and 2[sup]44[/sup]
k=3*7*311

M1234567890911 has a factor: 335802466327793
k=2[SUP]3[/SUP]*17
This is the only factor less than 2[SUP]65[/SUP]

M8675309 has a factor: 36297492857
M8675309 has 1 factor in [2[SUP]23[/SUP], 2[SUP]40[/SUP]-1].
k=2[SUP]2[/SUP]*523

M9876543211 has a factor: 93155555566153
M9876543211 has 1 factor in [2[SUP]33[/SUP], 2[SUP]65[/SUP]-1].
k=2[SUP]2[/SUP]*3[SUP]2[/SUP]*131

M9000000001 has a factor: 14076558001564063
M9000000001 has 1 factor in [2[SUP]33[/SUP], 2[SUP]60[/SUP]-1].
k=3*260677

[QUOTE=Stargate38;277363]I use Factor5 to find my factors:

M77,345,993 has a factor: 1010293360567
.....
M1,234,567,890,911 has a factor: 335802466327793
.....
M8,675,309 has a factor: 36297492857
......
M9,876,543,211 has a factor: 93155555566153
......
M9,000,000,001 has a factor: 14076558001564063[/QUOTE]
Before you test a number below 999,999,999 please use PrimeNet to check it out. Everything above 10,000,000 and below 1,000,000,000 have been taken to at least 64 bits. (We don't want you duplicating or wasting effort.) And submit your results.

If you are working from 3,321,928,097 to around 3,400,000,000 please check in with the [URL="http://mersenneforum.org/forumdisplay.php?f=50"]Operation Billion Digit forum [/URL].

If you are working outside these areas please follow the advice that you have previously been given:
"You should report any non-trivial results to Will Edgington, as well as the effort (how far they were taken) that was applied to the various numbers."

Smallest and largest from the last couple weeks of P-1 on small exponents, otherwise nothing special:

M3503971 has a factor: 12726397236394193321 (64 bits)
k = 2^2 x 5 x 192 x 587 x 428489

M3187733 has a factor: 19127766360473471950278162960119 (104 bits)
k = 139 x 1499 x 4783 x 11149 x 85601 x 3154429

ECM found a factor in curve #2, stage #2
Sigma=327809089600403, B1=50000, B2=5000000.

M846427 has a factor: 125946848143439048087 (67 bits)

k = 59 x 1261002036451

Another kill in the low 60Ms
 

M60011033 has a factor: 64002637955950819404341833.

Found in P-1 Stage 2, 85.726 bits. k = 2^2 x 3^2 x 7^2 x 11 x 227 x 241 x 443 x [B]1,133,963[/B]. What's the opposite of smooth? Crunchy? :smile:

ECM found a factor in curve #5, stage #2
Sigma=7739711815357313, B1=50000, B2=5000000.

M849833 has a factor: 26880181928765762327 (65 bits)

k = 15814978901011 (prime)

I like the "7,8,9,10,11" in that k :smile:

Am I crazy?
 

So, long story short, I'm playing with programming and mersenne numbers like most of you.

checking on factors on the low end Mnums and found 2 missing so far...

2^29 -1 [233,1103,[B][U]2089[/U][/B]]]
2^43 -1 [431,9719,[B][U]2099863[/U][/B]]

Is this an oversight?

sorry if i'm in the wrong spot, first day at forum

No. If you've listed all the smaller factors, then, once you've divided them out of the original number, you get the largest factor. Basically, listing the largest factor of the number is redundant. That's why they are not listed.

I would add to what axn said, last factor is usually much bigger then the others. Letting it unlisted also save space on the database, and makes printing of the other factors look nicer. Like for example M409, it has two small factors and then the last factor about 100 digits. It makes no sense to print that one on Primenet. You can find all of them for small exponents on [URL="http://factorization.ath.cx/index.php?query=2%5En-1"]factorDB [/URL]if you need.

edit: There [B]could be[/B] missing factors for small exponents on the Primenet DB, and you can try to find part of them if you are interested in programming and want to play with small exponents (to learn how it's working, or whatever reason you might have).

Long time ago, in the beginning of this project, small exponents (say below 1 million, or so) were eliminated from the candidate's list immediately after a factor was found. Later on, nobody bothered with exponents which already had known factors, because everybody was interested in finding mersenne primes, not finding factors of already (partially) factored mersenne numbers.

Programs that we currently use today are not anymore able to handle (or to get as assignments) such small exponents (for example mfaktX will refuse to handle any expo smaller then a million, etc). So, in the very lower range (exponents below 1,2,3,few millions) there should be some "missing" factors, for exponents whose corespondent mersenne number [B]already[/B] has other small factors. If you are interested in finding [B]these[/B] missing factors, then you can still look for them.

Caution, however: they (the factors) should be higher then 2^39 for exponents below 100k and higher then 2^48 for exponents between 100k and 1M. Below these values you can find all the factors for all the exponents in less then two days with few lines written in pari/gp (searching by the size of the factor, and not by exponent, discussed somewhere here around on the forum in another topic) and I believe all these factors are known to Primenet already (except they are not printed if they are the highest factor for some exponent, as you already were finding out).

We are talking here only about mersenne numbers which [B]already[/B] have known small factors. SG-prime exponents of the form 4k+3 should be a good place to start, as all these mersenne are divisible by 2*p+1, so all of them were eliminated in the very beginning, and no one checked for higher factors ever (well, almost, see Axon's thread somewhere around).

For the mersennes which are known to be composites but have no known factors, the limits are much higher, and you can see them on the primenet "[URL="http://www.mersenne.org/report_factoring_effort/"]how far factored[/URL]" page. For these, you have to go higher then the values in the table if you want to have any chance of finding a factor.

[QUOTE=LaurV;281597]Programs that we currently use today are not anymore able to handle (or to get as assignments) such small exponents (for example mfaktX will refuse to handle any expo smaller then a million, etc). So, in the very lower range (exponents below 1,2,3,few millions) there should be some "missing" factors, for exponents whose corespondent mersenne number [B]already[/B] has other small factors. If you are interested in finding [B]these[/B] missing factors, then you can still look for them.[/QUOTE]Factor5 can test low numbers.

Good catch, but that was not the point. Who is going to test them? Are you?

[QUOTE=LaurV;281619]Good catch, but that was not the point. Who is going to test them? Are you?[/QUOTE]

Worse still. You're better off doing ecm on these low numbers. And GIMPS has already done a lot of ecm on them. So there is very little possibility of TF succeeding at these low numbers.

[QUOTE=axn;281624]And GIMPS has already done a lot of ecm on them[/QUOTE]
Pls note we were talking about numbers with some factors known already. There is not "so much" ECM done for them, all the forces are/were concentrated on numbers with no known factors (like M1061 and its bigger brothers), for which I already specified the futility of trial factoring. The lots of ECM done for them is an additional reason why TF is futile here, as you said.

But for numbers with [B]already known[/B] factors, not so many people bothered to find additional factors, as the compositeness is "already clear". Usually the TF process stopped when a factor was found (we are talking "old times", the "Age of Legends" of GIMPS), and since then, no one bothered anymore with the respective exponents. There could still be place to dig, for curiosity, or other reasons (see the [URL="http://www.mersenneforum.org/showthread.php?t=15690"]Axon's thread[/URL]). Here, if someone would be interested in programming/testing/understanding how things work, etc, as OP said, or be interested in that small factors effectively, he could try to play. I believe any of us started long ago with trying to write TF programs for small factors and small exponents, these are the simplest things to program, and you still can learn a lot from it. (not you, axn,:P, I mean generally)

Well, forget about the 2^39, respectively 2^48, which I mentioned before. It seems as ALL exponents below 7.06M were TF-ed to 2^60, regardless of the fact that they had or they had not, any known factor. At least this can be seen from some [URL="http://www.mersenneforum.org/showpost.php?p=45176&postcount=64"]older threads here around[/URL], where people also talked this subject 6-7 years ago.

So, there should be [B]no missing factor[/B] below 2^60 for expos below 7.06M. You have to look at higher bitlevels, and/or higher expos to have any chance to get a new factor for the low-range expos.

Thanks for all the information!

I have a hypothesis that isn't panning out well right now, so I've been practicing mathematical coding and watching the numbers play out. It is remarkably easy to code the TF method. Efficient? No. Effective, yes. Plus I enjoyed watching my readout as my program ran.

I can completely understand not listing the 100 digit primes to save space. It seems odd to me that some factors aren't explicitly written though. Is that a local tradition? Or just a more concise way of writing factors that my limited scholastic experience never reached?

Is there a "complete" list of factors of Mersenne Numbers somewhere out there?
GIMPS (understandably) only pays attention to the p = prime exponents.

[QUOTE=zchacrea;281771]Is there a "complete" list of factors of Mersenne Numbers somewhere out there? GIMPS (understandably) only pays attention to the p = prime exponents.[/QUOTE]

[URL="http://www.garlic.com/~wedgingt/mersenne.html"]Will Edgington's Mersenne Page[/URL]

Note that algebraic factors are not repeated, so you will need to factor the exponent and look up the factorization of algebraic factors separately.

[QUOTE=zchacrea;281771]I can completely understand not listing the 100 digit primes to save space. It seems odd to me that some factors aren't explicitly written though.[/QUOTE]The only deliberately unwritten factor is the largest factor of a completely-factored number. That factor's value can easily be computed by dividing the number by the product of all the other factors.

Since you can understand not listing a 100-digit prime to save space, isn't it just as easy to understand not listing a 99-digit, 98-digit, 97-digit, or any other length final (prime) factor for the same reason?

[quote]Is that a local tradition?[/quote]Local to mathematics :-)

[quote]Or just a more concise way of writing factors that my limited scholastic experience never reached?[/quote]Keep in mind that the tradition was established many years ago (as were almost all mathematical traditions) when factors were more commonly being written by hand.

On mersenne.org, is there a simple way to tell which mersenne numbers are completely factored? All I can work out is it ought to be the ones on the known factors page that aren't on the ECM progress page.

[QUOTE=markr;282116]On mersenne.org, is there a simple way to tell which mersenne numbers are completely factored?[/QUOTE]AFAIK the only way is to start by looking at the "Factoring Limits" report, and note which prime exponents are NOT listed there. Mersenne numbers with prime exponents that are NOT listed in the "Factoring Limits" report are either prime or have been completely factored.

Then, one has to compare the list of exponents NOT in the "Factoring Limits" report with the list of exponents that ARE on the "Known Primes" list, and subtract the latter from the former to get the list of completely-factored numbers.

Oh ... you specified "simple" ...

No.

[quote]All I can work out is it ought to be the ones on the known factors page that aren't on the ECM progress page.[/quote]... but that would presume that the ECM progress page lists all not-yet-factored ones. It doesn't; it lists only exponents for which [i]there has been at least one ECM effort[/i].

[QUOTE=cheesehead;282138]AFAIK the only way is to start by looking at the "Factoring Limits" report, and note which prime exponents are NOT listed there. Mersenne numbers with prime exponents that are NOT listed in the "Factoring Limits" report are either prime or have been completely factored.[/QUOTE]?? I thought an exponent was removed from the factoring limits report when even one factor was found. That report is the starting-point when getting one's choice of LMH-type work.

[QUOTE]... but that would presume that the ECM progress page lists all not-yet-factored ones. It doesn't; it lists only exponents for which [i]there has been at least one ECM effort[/i].[/QUOTE]Thanks for that information.

Given there's no "completely-factored" flag in the mersenne.org reports (AFAIK) I think we'll have to count comparing two lists as simple enough. :whistle:

M54844001 has a factor: 1588991208980582426527
k= 3^2 * 13 * 23 * 5383301093 would have been very hard to find with P-1

[QUOTE=markr;282116]On mersenne.org, is there a simple way to tell which mersenne numbers are completely factored?[/QUOTE]

The two places I would check for completed factorizations are [URL="http://www.garlic.com/~wedgingt/mersenne.html"]Will Edginton's Mersenne Page[/URL] and [URL="http://www.factordb.com/"]factordb[/URL]. If you find a number fully factored in only one of these, I recommend informing the other (email to Will or add the factor to factordb).

[QUOTE=markr;282156]?? I thought an exponent was removed from the factoring limits report when even one factor was found.[/QUOTE][U][b]You're absolutely right !![/U][/b]

I was mixing up ... oh, never mind ...

There is no method within GIMPS.

Here's our first contestant for the Biggest Factor Of 2012 contest: :judge:

M7113559 has a factor: 209608785077907609615323945622290057 [118 bits]

k = 2^2 * 7^2 * 13^2 * 1753 * 26017 * 42899 * 152083 * 1494799

P-1, B1=450000, B2=13837500

all time (prime) high
 

Is this still our all time (prime) high? (only in this thread) Found in 2011...

[QUOTE=ckdo;254250]M13828261 has a factor: 1979553586274192263311048622055057969

121 bits [I]and [/I]prime. :groupwave:

k = 2^3*13*71*397*160751*262651*556559*1039067[/QUOTE]

Beat this...

[QUOTE=Brain;284635]Is this still our all time (prime) high? (only in this thread) Found in 2011...



Beat this...[/QUOTE]


I believe my find in post #196 is a little larger.

Doug

[QUOTE=drh;269697]... and appears to be the largest in this thread-

M56226553 has a factor: 134624114590567994209661373751147664039

It is prime, and k = 1197157814303217149108014622123
= 7 × 5717 × 26371 × 29101 × 70051 × 104677 × 5316001

126.662 bits[/QUOTE]

How could I miss that... Sorry. Beat this!

[SIZE=2]M29044087 heas a factor : [/SIZE][SIZE=2]377831049605863523519

[/SIZE]k=47*191*724567241
(68.356 bit)
thanks gpu to 72!
I saved you about 28Ghz/day of work
also, my first factor of 2012.

M7175153 has a factor: 7445119556513212989927121 [83 bits]

k = 2^3 * 3^5 * 5 * 7 * 113 * 569 * 118,592,029

P-1, stage 2, B1=455000, B2=13991250, E=12

M2349679 has a factor: 560951511036414812113
Found by P1 Stage 2, B1=155000, B2=3565000

k = 2^3 × 3 × 347^2 × 6427^2

or

k = 2^3 x 3 x 120,409 x 41,306,329

[QUOTE=harlee;285834]M2349679 has a factor: 560951511036414812113
Found by P1 Stage 2, B1=155000, B2=3565000
k = 2^3 × 3 × 347^2 × 6427^2
[/QUOTE]
Very nice finding, with all those squares! Handsome!

I am running P-1 using B1 = 10M and B2 = 200M on the 3xxxxx range. I found some factors, but this is interesting:

M325517 has a factor: 20823082720665516480026432503
k = 3 ^ 3 x 107 x 223 x 9805721 x 5063017369

The second greatest prime factor is just below B1 and the greatest prime factor is more than 25 times B2.

[QUOTE=ckdo;285810]M7175153 has a factor: 7445119556513212989927121 [83 bits]

k = 2^3 * 3^5 * 5 * 7 * 113 * 569 * 118,592,029

P-1, stage 2, B1=455000, B2=13991250, E=12[/QUOTE]


Wow. Brent-Suyama found it? That's the first I've seen it.

[QUOTE=alpertron;286366]I am running P-1 using B1 = 10M and B2 = 200M on the 3xxxxx range. I found some factors, but this is interesting:

M325517 has a factor: 20823082720665516480026432503
k = 3 ^ 3 x 107 x 223 x 9805721 x 5063017369

The second greatest prime factor is just below B1 and the greatest prime factor is more than 25 times B2.[/QUOTE]

Same here, it would seem.

[QUOTE=Brain;284711]How could I miss that... Sorry. Beat this![/QUOTE]

M50,232,683 has a factor: [URL="http://mersenne-aries.sili.net/exponent.php?factordetails=3312819927398148201283212927854847645967"][COLOR=#0066cc]3312819927398148201283212927854847645967[/COLOR][/URL]

k= 3[SIZE=2][SUP][SIZE=2]2[/SIZE][/SUP] × 487 × 503 × 691 × 45497 × 248161 × 404507 × 4739381[/SIZE]

I found it December 18, 2011. 40 digits, 132 bits. The link takes you to Mersen-aires.

B2 saturation
 

[QUOTE=Chuck;287032]M50,232,683 has a factor: [URL="http://mersenne-aries.sili.net/exponent.php?factordetails=3312819927398148201283212927854847645967"][COLOR=#0066cc]3312819927398148201283212927854847645967[/COLOR][/URL]

k= 3[SIZE=2][SUP][SIZE=2]2[/SIZE][/SUP] × 487 × 503 × 691 × 45497 × 248161 × 404507 × 4739381[/SIZE]

I found it December 18, 2011. 40 digits, 132 bits. The link takes you to Mersen-aires.[/QUOTE]
Awesome. Waiting for more to come...

Meanwhile, I post my closest B2 find so far, B2 was 14,066,250:
[CODE]M56605037 has a factor: 11454648301977844461209
k = 2 * 2 * 31 * 58417 * 13968049
Saturation(B2) = 0.993 = 13968049 / 14066250[/CODE]

What's the rule for composites?
[url]http://mersenne-aries.sili.net/exponent.php?exponentdetails=52567117[/url]
5^2 × 67 × 389 × 607 × 240631
2^2 × 5 × 13 × 17 × 113 × 3581 × 4517 × 7507

73 and 82 bits respectively (total=155)

And dang, 0.993 is ridiculously close to 1, that's gonna be hard to beat

Morning glory
 

M7293457 has a factor: 533975545077050000610542659519277030089249998649 [159 bits]
= 114899029154970496577 [67 bits] * 4647346013314424799552178937 [92 bits]

k1 = 2^5×7×19433×1809527
k2 = 2^2×7×17×29×227×1103×126499×728699

P-1 S2, B1=460000, B2=14260000

Wow. That's big.

Congratulations Michel Kenn
 

[URL="http://www.kenn.at/"][COLOR=#0066cc]Michael Kenn[/COLOR][/URL] Manual testing 1721 F-ECM Feb 3 2012 4:45PM 0.0 0.0000 13017424887805605413748227640619647231549577734497

5th largest factor found since 2011-01-01
Factor of M1721

Michael Kenns factor is in place 69 ever
 

Michael Kenns factor found yesterday is the 69th largest of all prime factors found ever of Mersenne numbers with prime exponent. Well done!

M58121533 has a factor: 4587597268738219322985479392479497743
121.78 Bits; k = 39465556326071262805348573587 = 3[SUP]2[/SUP] * 7[SUP]3[/SUP] * 17 * 131 * 727 * 1039 * 53309 * 81727 * 1744397

My new personal record and my first P-1 factor >2[SUP]120[/SUP].

Congrats
 

[QUOTE=TheJudger;288382]M58121533 has a factor: 4587597268738219322985479392479497743
121.78 Bits; k = 39465556326071262805348573587 = 3[SUP]2[/SUP] * 7[SUP]3[/SUP] * 17 * 131 * 727 * 1039 * 53309 * 81727 * 1744397

My new personal record and my first P-1 factor >2[SUP]120[/SUP].[/QUOTE]
:groupwave:

[QUOTE=TheJudger;288382]M58121533 has a factor: 4587597268738219322985479392479497743
121.78 Bits; k = 39465556326071262805348573587 = 3[SUP]2[/SUP] * 7[SUP]3[/SUP] * 17 * 131 * 727 * 1039 * 53309 * 81727 * 1744397

My new personal record and my first P-1 factor >2[SUP]120[/SUP].[/QUOTE]

[URL="http://mersenne-aries.sili.net/exponent.php?exponentdetails=58121533"]Link[/URL] to James' site. Awesome find!

[QUOTE=Chuck;287032]M50,232,683 has a factor: [URL="http://mersenne-aries.sili.net/exponent.php?factordetails=3312819927398148201283212927854847645967"][COLOR=#0066cc]3312819927398148201283212927854847645967[/COLOR][/URL][/QUOTE]

Just for amusement, I've created a quick report showing the [URL="http://www.gpu72.com/reports/largest_factors/"]Top 100 Factors Found[/URL] by G72 workers.

[QUOTE=chalsall;288393]Just for amusement, I've created a quick report showing the [URL="http://www.gpu72.com/reports/largest_factors/"]Top 100 Factors Found[/URL] by G72 workers.[/QUOTE]

Ok, that's cool. Are they all P-1?

[QUOTE=flashjh;288396]Ok, that's cool. Are they all P-1?[/QUOTE]

The query doesn't limit it to P-1 only, but yes, everything you see there was found by P-1.

Even with a GPU, it would be silly to TF to 82... :wink:

Another report I've been thinking about is a [URL="http://www.gpu72.com/reports/factorihttp://www.gpu72.com/reports/factoring_cost/p-1/ng_cost/p-1/"]Cost per Factor Found[/URL] (like already exists for TF) for P-1 as a function of Exponent level and previous TFed level.

[QUOTE=chalsall;288397]Another report I've been thinking about is a [URL="http://www.gpu72.com/reports/factoring_cost/p-1/"]Cost per Factor Found[/URL] (like already exists for TF) for P-1 as a function of Exponent level and previous TFed level.[/QUOTE]

Sigh... I need to get a new mouse... This one randomly pastes twice.

[url]http://www.gpu72.com/reports/factoring_cost/p-1/ng_cost/p-1/[/url]

Could not find the page. The link is broken, and I did my best to fix it (getting what's above) but that didn't work either.

[QUOTE=Dubslow;288410]Could not find the page. The link is broken, and I did my best to fix it (getting what's above) but that didn't work either.[/QUOTE]

Yes, I know. If you click on the link in my follow up post (where I obviously wasn't clear enough) you'll get the correct page.

To be explicit, it's [URL="http://www.gpu72.com/reports/factoring_cost/p-1/"]http://www.gpu72.com/reports/factoring_cost/p-1/[/URL]

My first two factors
 

M802450937 has a factor: 27253075353941008183 (64.6 bits)
M802439791 has a factor: 69211649764401219511 (65.9 bits)

These are first two factors I found since I participate GIMPS.

We have another Brent-Suyama
[url]http://mersenne-aries.sili.net/exponent.php?exponentdetails=52827883[/url]

I'm 99% sure E=12

M12004387 has a factor: 31857018725491979850118505288637023 (115 bits)
P-1 found a factor in stage #2, B1=230000, B2=5635000
k=97 × 307 × 5693 × 7621 × 11827 × 19477 × 4458361

M56840527 has a factor: 87985788014528609178889 (76.2 bits)
Found in Stage 1 of P1
K = 2^2 × 3^3 × 151 × 379 × 409 × 306169

[Feb 26 13:12] Optimal P-1 factoring of M54570709 using up to 3000MB of memory.
[Feb 26 13:12] Assuming no factors below 2^71 and 2 primality tests saved if a factor is found.
[Feb 26 17:19] P-1 found a factor in stage #2, B1=575000, B2=12937500.
[Feb 26 17:19] M54570709 has a factor: 21773037347664618203527

Welcome
 

[QUOTE=Stef42;290956][Feb 26 13:12] Optimal P-1 factoring of M54570709 using up to 3000MB of memory.
[Feb 26 13:12] Assuming no factors below 2^71 and 2 primality tests saved if a factor is found.
[Feb 26 17:19] P-1 found a factor in stage #2, B1=575000, B2=12937500.
[Feb 26 17:19] M54570709 has a factor: 21773037347664618203527[/QUOTE]
Congrats and welcome to GIMPS forum! We'd like to know the fingerprint / value of k. ;-) It can be calculated as described here: P-1 factoring at [URL]http://www.mersenne.org/various/math.php[/URL]

The factorisation can be done here: [URL]http://mersenne-aries.sili.net/factor.php[/URL]

or here: [url]http://wims.unice.fr/wims/wims.cgi?cmd=new&module=tool/algebra/factor.en[/url]

[Feb 27 05:48] Stage 2 GCD complete. Time: 48.982 sec.
[Feb 27 05:48] P-1 found a factor in stage #2, B1=425000, B2=8181250.
[Feb 27 05:48] M[URL="http://mersenne-aries.sili.net/exponent.php?exponentdetails=47493847"]47493847[/URL] has a factor: 2774014039648646760250409

k = 2[SIZE=2][SUP][SIZE=2]2[/SIZE][/SUP] × 29 × 18313 × 23567 × 583337[/SIZE]

[QUOTE=Brain;290968]Congrats and welcome to GIMPS forum! We'd like to know the fingerprint / value of k. ;-) It can be calculated as described here: P-1 factoring at [URL]http://www.mersenne.org/various/math.php[/URL]

The factorisation can be done here: [URL]http://mersenne-aries.sili.net/factor.php[/URL][/QUOTE]

From: [url]http://mersenne-aries.sili.net/exponent.php?exponentdetails=M54570709[/url]

K: = 3 × 13 × 529747 × 9655979

I hope I've done this right, I'm not all too well in math (ironically), just helping a bit :)

thats a nice one, close to max B1 and B2.

[QUOTE=Stef42;291095]From: [URL]http://mersenne-aries.sili.net/exponent.php?exponentdetails=M54570709[/URL]

K: = 3 × 13 × 529747 × 9655979

I hope I've done this right, I'm not all too well in math (ironically), just helping a bit :)[/QUOTE]Yes, that's correct. So, that K * 2 * 54570709 + 1 = 21773037347664618203527

Remarkably not-smooth factor, yet as firejuggler points out, it was still just smooth enough to be found.

Brent-Suyama 0_o

[url]http://mersenne-aries.sili.net/exponent.php?factordetails=3546977485247966555997217[/url]

:mellow:

k = 2^4 × 3 × 1367 × 1427 × [U][B]346 268 953[/B][/U] (81.55 bits)

B2 = 8,906,250;
factor = 346,268,953

factor/B2 = 38.9

For every other expo on this comp, E=12, but P95 doesn't report E when a factor is found.

[CODE][Sat Mar 03 19:13:28 2012]
ECM found a factor in curve #2, stage #1
Sigma=4837041697745753, B1=50000, B2=5000000.
M6597233 has a factor: 200133817910449865999, AID: 919ABE49609E1C6F151B5D84F6E6435A[/CODE]

[url]http://mersenne-aries.sili.net/exponent.php?exponentdetails=6597233[/url]

k = 1423 × 10659179161

[URL="http://mersenne-aries.sili.net/exponent.php?exponentdetails=52654237"]M52654237[/URL]
factor: 15207934150978277088314271047
digits: 29
bits: 93.619
k = 17 × 131 × 149 × 281 × 1433 × 5741 × 188261

Another prime k
 

Found via mfaktc 0.18:
M(2,054,449) has a factor: [SIZE=2]2318907894154523879 (61.0 bits)[/SIZE]
k = 564362487011 (prime)

Nice prime k.

[url]http://mersenne-aries.sili.net/exponent.php?exponentdetails=46800163[/url]
k=2^2 × 7 × 11 × 19 × 15 413 × 48 733 × 4 668 371
90.6 bits, and my biggest factor to date.

M55790419 has a factor: 1247190322545119514889 [TF:70:71:mfaktc 0.18 barrett79_mul32]
found 1 factor for M55790419 from 2^70 to 2^71 [mfaktc 0.18 barrett79_mul32]

k = 2[SUP]2[/SUP] × 3[SUP]2[/SUP] × 89 × 3488595419

70.079 bits.

4 more -

M57020807 has a factor: 3160553444946253221751
k=27714036430125 = 3^2 × 5^3 × 29 × 37 × 83 × 163 × 1697
71.421 bits

M57694789 has a factor: 5317864403454508773223125673
k=46086176027565581124 = 2^2 × 3 × 7 × 47 × 1013 × 2371 × 19259 × 252359
92.103 bits (Good size, but nowhere near my largest)

M76171231 has a factor: 3917541776227745260849
k=25715363430504 = 2^3 × 3 × 11 × 3853 × 4349 × 5813
71.730 bits

M76145807 has a factor: 2635433273541907685207
k=17305176590629=[B][COLOR=red]PRIME[/COLOR][/B]
71.159 bits

You're missing some carets ^ fyi

Found a nice one.
Not my largest factor, but close.

[URL="http://mersenne-aries.sili.net/exponent.php?exponentdetails=55349207"]M55349207[/URL]

[CODE]
[Fri Mar 23 12:02:58 2012]
P-1 found a factor in stage #2, B1=480000, B2=9240000, E=12.
UID: flashjh/TF2, M55349207 has a factor: 8529147885804847640875839764743
[/CODE]

k = 3 × 197 × 11897 × 16823 × 399221 × 1631633
Digits = 31
Bits= 102.750