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-   -   Found a factor? Post it here. (https://www.mersenneforum.org/showthread.php?t=13977)

 c10ck3r 2011-08-05 13:46

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

 drh 2011-08-21 17:14

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

 harlee 2011-08-28 12:30

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

 ckdo 2011-09-04 21:18

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]

 TheJudger 2011-09-13 16:02

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)

 diamonddave 2011-09-16 12:18

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

 alpertron 2011-09-24 22:51

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

 Chuck 2011-09-29 02:31

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]

 harlee 2011-10-01 12:17

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.

 harlee 2011-10-02 15:31

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

 Chuck 2011-10-08 12:43

[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]

 TheJudger 2011-10-08 12:51

[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

 Chuck 2011-10-08 13:12

[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

 lorgix 2011-10-08 13:32

[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]

 Chuck 2011-10-08 13:37

[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]

Chuck

 lorgix 2011-10-08 13:47

[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]

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.

 Mr. P-1 2011-10-08 16:03

[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.

 Uncwilly 2011-10-08 16:08

[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]

 lorgix 2011-10-08 16:17

[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

 Mr. P-1 2011-10-09 08:57

[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.

 Mr. P-1 2011-10-09 09:01

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?

 harlee 2011-10-19 23:00

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

 Brain 2011-10-20 18:06

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]

 harlee 2011-11-04 02:45

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.

 Lorenzo 2011-11-06 09:25

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

My first factor :big grin:

 Stargate38 2011-11-06 16:29

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

 Uncwilly 2011-11-07 00:32

[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."

 markr 2011-11-19 06:23

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

 ckdo 2011-11-23 06:31

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

 NBtarheel_33 2011-11-23 10:38

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:

 ckdo 2011-11-28 07:55

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:

 zchacrea 2011-12-08 16:59

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

 axn 2011-12-08 18:21

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.

 LaurV 2011-12-09 02:50

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.

 Uncwilly 2011-12-09 04:27

[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.

 LaurV 2011-12-09 05:44

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

 axn 2011-12-09 06:07

[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.

 LaurV 2011-12-09 07:28

[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)

 LaurV 2011-12-10 04:06

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.

 zchacrea 2011-12-10 15:12

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.

 wblipp 2011-12-13 14:40

[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.

 markr 2011-12-13 23:57

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].

 markr 2011-12-14 08:33

[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:

 firejuggler 2011-12-14 20:22

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

 wblipp 2011-12-15 16:09

[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.

 ckdo 2012-01-03 07:28

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

 Brain 2012-01-03 19:57

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...

 drh 2012-01-03 22:07

[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

 Brain 2012-01-04 06:40

[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!

 firejuggler 2012-01-04 08:18

[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.

 ckdo 2012-01-10 22:26

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

 harlee 2012-01-11 01:35

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

 LaurV 2012-01-11 02:20

[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!

 alpertron 2012-01-15 15:31

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.

 Dubslow 2012-01-16 14:47

[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.

 Chuck 2012-01-23 13:36

[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.

 Brain 2012-01-25 18:18

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]

 Dubslow 2012-01-26 04:19

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

 ckdo 2012-01-26 10:20

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

 Dubslow 2012-01-27 04:06

Wow. That's big.

 aketilander 2012-02-04 17:00

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

 aketilander 2012-02-04 17:08

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!

 TheJudger 2012-02-05 17:10

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].

 Brain 2012-02-05 17:39

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:

 flashjh 2012-02-05 17:50

[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!

 chalsall 2012-02-05 19:01

[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.

 flashjh 2012-02-05 19:54

[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?

 chalsall 2012-02-05 20:06

[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.

 chalsall 2012-02-05 22:01

[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.

 Dubslow 2012-02-05 22:46

[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.

 chalsall 2012-02-05 22:51

[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]

 dabaichi 2012-02-11 02:11

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.

 Dubslow 2012-02-18 04:58

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

I'm 99% sure E=12

 harlee 2012-02-26 13:15

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

 gjmccrac 2012-02-26 13:58

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

 Stef42 2012-02-26 16:23

[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

 Brain 2012-02-26 18:19

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]

 flashjh 2012-02-27 14:35

[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]

 Stef42 2012-02-27 21:56

[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 :)

 firejuggler 2012-02-27 22:06

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

 Dubslow 2012-02-27 22:32

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

 Dubslow 2012-03-01 05:43

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.

 Stef42 2012-03-05 08:29

[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

 flashjh 2012-03-06 04:19

[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

 Brain 2012-03-11 12:51

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)

 Dubslow 2012-03-14 22:25

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.

 Stef42 2012-03-19 21:23

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.

 drh 2012-03-21 21:19

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

 Dubslow 2012-03-21 21:23

You're missing some carets ^ fyi

 flashjh 2012-03-23 23:19

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

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