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

 LaurV 2014-11-20 11:27

I digested what the server gave me.
I have stopped anyhow, after I found that factor, and concentrate now on DCTF, after the last arguments in the GPU72 thread.

 lycorn 2014-11-20 12:40

That´s right, exponents handed by the server for ECM are in the 9M range. I wonder why so high. That´s why I get them manually.
Just out of curiosity, when you say you gave up ECM to concentrate on DCTF does that mean you are moving CPU(s) to DCTF, or you were using some program that would allow running ECM on a GPU? Or...?

 VictordeHolland 2014-11-20 15:10

IIRC 2^1018-1 is still the maximum GPU-ECM can handle.

The difficulty with determining the desired TF level before running ECM lies with the differences in CPU and GPU capabilities and available resources. On ECM candidates with no (or very few) curves you MIGHT be better off running TF a bit deeper IF you have the GPU resources available (which should really be doing DCTF and LLTF). I personally wouldn't recommend running TF on anything <10M, since most of those have had a fair share of P-1 and ECM.

 lycorn 2014-12-02 18:48

Look at this one:

[I]ECM found a factor in curve #181, stage #2
Sigma=3947118002300977, B1=250000, B2=25000000.
UID: lycorn/asteroid, M507149 has a factor: 1834049842474634749280697499913 (ECM curve 181, B1=250000, B2=25000000)
[/I]
Factor is prime, and its k=2[SUP]2[/SUP] × 452049063114251124738661

Only ECM could have found it...

 legendarymudkip 2014-12-02 22:25

M70637093 has a factor: 27886899376721683540674433 (84.5 bits)
k=2[SUP]6[/SUP] × 3[SUP]3[/SUP] × 7 × 11 × 13 × 23 × 7877 × 629899
k is pretty smooth and has a lot of very small factors.

 VictordeHolland 2014-12-03 14:47

P-1 stage 1 factor

A nice P-1 stage 1 factor popped up yesterday 91.5 bits (28 digits):

P-1 found a factor in stage #1, B1=1500000.
UID: VictordeHollander/PCVICTOR, M68842181 has a factor: 3483933495938630920516781759 (P-1, B1=1500000)

k = 25303770488754786259 = 7 × 11 × 977 × 12641 × 26777 × 993703

 Dubslow 2014-12-03 16:37

First a 2^2 * prime k, then an odd k...

 lycorn 2015-01-07 08:01

Another nice ECM finding:

[I]ECM found a factor in curve #407, stage #2
Sigma=361548692013119, B1=250000, B2=25000000.
UID: lycorn/asteroid, M507827 has a factor: 1011161162890642691485323460063 (ECM curve 407, B1=250000, B2=25000000)[/I]

k= 995576409772070696797653 =33 × 883 × 41759003807393594933

Totally out of reach for TF/P-1...

 TObject 2015-01-13 20:35

Somebody reported a TF factor for an exponent in the First LL range, just above the current recommended factoring limits:

M65840041 has a factor q=31805465644706384183591; log2(q)=74.752...
k = 5 * 47 * 1027812292817 = 241535888811995; log2(k)=47.779...
1027812292817/74.752 = 13749629345.26...

 TheJudger 2015-01-13 21:31

GPU to 72 hands out TF assignments to 2[SUP]75[/SUP].

 petrw1 2015-01-13 22:21

[QUOTE=TheJudger;392355]GPU to 72 hands out TF assignments to 2[SUP]75[/SUP].[/QUOTE]

And some people "choose" to go many bits higher even for much lower assignments

 TObject 2015-01-13 22:22

[QUOTE=TheJudger;392355]GPU to 72 hands out TF assignments to 2[SUP]75[/SUP].[/QUOTE]

Ok, then, I thought it was 74, as that is all I see. Thank you for the correction.

 TObject 2015-01-13 22:24

mersenne.ca reports that GPU72 Trial Factoring Limit for M65,840,041 is 73. Probably outdated info...

 LaurV 2015-01-14 06:05

Mersenne.ca is the "correct" limit.

[rant]
(Un)/Fortunately GPU72 and TGTB have seen the boosting on the factoring power and decided to raise some limits, even if the factoring to those limits is not very efficient (and it should be faster to directly LL, especially for the expos with P-1 done, but hey, finding factors is cool :razz:). Fortunately there are only (very) few exponents in this situation and we will get rid of them fast. More painful will be DCTF to 72/73 for the lower ranges (where there are LOTS of exponents, and far lower efficiency, maybe my calculus is in the weeds, but even[URL="http://www.gpu72.com/reports/estimated_completion/primenet/"] these tables[/URL] show that it will be faster to DC them directly.... for example at 60M, we would need 5 days to LL/DC everything, but we would need 9 days to take all to 75 bits...)
[/rant]

 chalsall 2015-01-14 18:33

[QUOTE=TObject;392359]mersenne.ca reports that GPU72 Trial Factoring Limit for M65,840,041 is 73. Probably outdated info...[/QUOTE]

Depends on the manufacturer and card... A Nvidia [URL="http://www.mersenne.ca/cudalucas.php?model=9"]"compute v2.0"[/URL] card, for example, is "profitable" going to 75.

 chalsall 2015-01-14 18:37

[QUOTE=LaurV;392373]...maybe my calculus is in the weeds, but even[URL="http://www.gpu72.com/reports/estimated_completion/primenet/"] these tables[/URL] show that it will be faster to DC them directly.... for example at 60M, we would need 5 days to LL/DC everything, but we would need 9 days to take all to 75 bits...)[/QUOTE]

You are comparing apples and oranges... The table you linked to shows the estimated completion if all resources were dedicated to a particular range based on the throughput for TF'ing and LL'ing.

James' analysis, on the other hand, shows where the optimal cross-over point is between using a GPU to do TF'ing vs. LL'ing.

 LaurV 2015-01-15 12:12

[QUOTE=chalsall;392433]You are comparing apples and oranges... The table you linked to shows the estimated completion[U] if all resources were dedicated to a particular range[/U] based on the throughput for TF'ing and LL'ing.[/QUOTE]
Like in "if all users of gpu72 would TF the 60M to 75 bits it would take 9 days, but if all users of gpu72 would LL the same 60M, they will finish in only 5 days" apples and oranges?
:razz:

 Mark Rose 2015-01-16 02:03

[QUOTE=LaurV;392373]but hey, finding factors is cool :razz:)[/QUOTE]

That's all I do :razz:

 legendarymudkip 2015-01-16 22:41

M252713 has a factor: 27595919843984963446046340023
k = 13 × 19 × 557 × 1621 × 3010541 × 81321913

Finally got something from all the P-1 I've been running on small numbers.

 storflyt32 2015-01-17 17:00

I guess lycorn meant to say

k= 995576409772070696797653 =3 × 3 × 3 × 883 × 41759003807393594933

on the previous page.

 lycorn 2015-01-18 02:04

Yep, you´re right. Sorry about the typo.

 legendarymudkip 2015-01-21 19:56

M442579 has a factor: 167564299150354202092313

A very rough k, 189304394413600964 = 2*2*47326098603400241.

 lycorn 2015-01-21 23:39

Wow!
ECM, for sure...

 LaurV 2015-01-22 02:28

[QUOTE=lycorn;393137]Wow!
ECM, for sure...[/QUOTE]
That's extremely easy ECM hit, 47326098603400241-9 factors as 2^3*7^2*11*29*101*1259*1289*2309

 lycorn 2015-01-22 08:31

Yes, but out of reach for TF/P-1.

 VictordeHolland 2015-01-22 10:55

I got two 100bit+ factors today with P-1 in the M1,50x,xxx range

P-1 found a factor in stage #1, B1=10000000.
UID: VictordeHollander/PC3770K, M1502201 has a factor: 9961858164484318845045819049537753539391 (P-1, B1=10000000)
k= 3315754071686917677809367404740695 = 3 × 5 × 37 × 101 × 29641 × 208513 × 955607 × 2035669 × 4919891
40 digits 132.872 bits

P-1 found a factor in stage #2, B1=10000000, B2=200000000, E=12.
UID: VictordeHollander/PC3770K, M1506287 has a factor: 269397059377600248844073196596567 (P-1, B1=10000000, B2=200000000, E=12)
k = 89424213107329562309199109 = 853 × 55829 × 72551 × 1958681 × 13214147
33 digits 107.731 bits

 legendarymudkip 2015-01-22 16:16

[QUOTE=LaurV;393151]That's extremely easy ECM hit, 47326098603400241-9 factors as 2^3*7^2*11*29*101*1259*1289*2309[/QUOTE]
I went slightly over the required bounds with B1=50k and B2=5M then :P

 VictordeHolland 2015-01-28 14:16

Already a few days old, but didn't notice until today:
[code]
[Sat Jan 24 20:35:50 2015]
P-1 found a factor in stage #2, B1=10000000, B2=200000000, E=12.
UID: VictordeHollander/PCVICTOR, M1511119 has a factor: 5764460914072987547513 (P-1, B1=10000000, B2=200000000, E=12)[/code]k = 1907348433205124 = 2^2 × 7^2 × 13 × 1277 × 586191769

minB2 586,191,769
found with B2=200,000,000 E=12

Brent-Suyama extention :smile:??

 PageFault 2015-02-03 01:47

Got another one today:

[CODE]ECM found a factor in curve #151, stage #2
Sigma=7925104694545819, B1=11000000, B2=1100000000.
UID: ANONYMOUS, M25111 has a factor: 5427507816547664928563953328692570691308025921
[/CODE]

k = 2^5 x 5 x 5153 x 7207 x 22171 x 17945173 x 45712910703677057947

 YuL 2015-02-07 11:01

M73012001

[CODE]
[Sat Feb 07 11:04:31 2015]
P-1 found a factor in stage #1, B1=825000.
UID: ****, M73012001 has a factor: 20078579801333391977956082839 (P-1, B1=825000)
[/CODE]

94.02 bits
k = 3×73×139×389×683×35267×482071

 VictordeHolland 2015-02-11 09:41

[code][Tue Feb 10 23:22:51 2015]
P-1 found a factor in stage #2, B1=10000000, B2=200000000, E=12.
UID: VictordeHollander/PCVICTOR, M1609063 has a factor: 688971262380939975396559401247 (P-1, B1=10000000, B2=200000000, E=12)[/code]30 digits, 99.12 bits
k = 214090828755909487508121 = 3 × 19 × 223 × 6,343 × 4,351,547 × [B]610,210,891
[/B]Another B-S!

 alpertron 2015-02-12 12:48

[QUOTE=LaurV;393151]That's extremely easy ECM hit, 47326098603400241-9 factors as 2^3*7^2*11*29*101*1259*1289*2309[/QUOTE]

It is easy only if your computer selects one of the lucky values of sigma for which the group order is the number you mentioned.

 YuL 2015-02-12 20:25

M73012031

[CODE]
[Thu Feb 12 16:22:15 2015]
P-1 found a factor in stage #2, B1=825000, B2=24000000, E=6.
UID: ****, M73012031 has a factor: 43976881458608153910283872823715921 (P-1, B1=825000, B2=24000000, E=6)
[/CODE]

115.082 bits
k=2^3 × 5 × 13 × 173 × 1777 × 246689 × 464549 × 16439243

 lycorn 2015-03-01 13:11

Look at this beauty:

[I]ECM found a factor in curve #1168, stage #2
Sigma=6873794231931630, B1=11000000, B2=1100000000.
UID: lycorn/asteroid, M20011 has a factor: 187852747203883018784775678996501624848413313 (ECM curve 1168, B1=11000000, B2=1100000000),
[/I]

147.074 bits

K = 2[SUP]6[/SUP] × 541 × 3547 × 489113 × 39334897501 × 1986520754106589

I threw all 4 cores of an i5-750 at it, running a total of ~5000 curves.

 bloodIce 2015-03-01 21:18

[QUOTE=lycorn;396731]Look at this beauty:

[I]ECM found a factor in curve #1168, stage #2
Sigma=6873794231931630, B1=11000000, B2=1100000000.
UID: lycorn/asteroid, M20011 has a factor: 187852747203883018784775678996501624848413313 (ECM curve 1168, B1=11000000, B2=1100000000),
[/I]

147.074 bits

K = 2[SUP]6[/SUP] × 541 × 3547 × 489113 × 39334897501 × 1986520754106589

I threw all 4 cores of an i5-750 at it, running a total of ~5000 curves.[/QUOTE]

Super nice find! Untouchable by Pm1. I wish more people are throwing all 4 in these "small" exponents. Keep the factors coming.

 lycorn 2015-03-01 23:39

[QUOTE=bloodIce;396760] Keep the factors coming.[/QUOTE]

Well, finding factors this large is hard. It takes a lot of curves to get one.
I´m currently putting M11423 through the same process. There are still 4000 curves to run @B1=11000000. If nothing comes up. I´ll move to B1=44000000. But that yes, will be really tough...

 petrw1 2015-03-02 23:02

I've never reported a factor here; should I?

Any I find will be reported to PrimeNet (Prime95); is there any reason they can't be found there and need to be reported here specifically?

 Prime95 2015-03-02 23:21

[QUOTE=petrw1;396832]Any I find will be reported to PrimeNet (Prime95); is there any reason they can't be found there and need to be reported here specifically?[/QUOTE]

No, this thread is solely for "bragging" about a found factor. One can brag for any number of reasons, very large factors, factors with unusual P-1 factorizations, factors barely above the TF level, etc.

 Dubslow 2015-03-02 23:28

Once, back even before I was a semimod, this thread had a vaguely descriptive title. :smile:

 Prime95 2015-03-02 23:39

[QUOTE=Dubslow;396834]Once, back even before I was a semimod, this thread had a vaguely descriptive title. :smile:[/QUOTE]

The title hasn't changed in over a year, time to begin another round of changes....

 Dubslow 2015-03-03 01:32

[QUOTE=Prime95;396836]The title hasn't changed in over a year, time to begin another round of changes....[/QUOTE]

Unfortunately "lost prosperity office" is now seared in my head.

 alpertron 2015-03-04 17:44

Very smooth prime factor of M1497577: 413967618533674438312273239368161 (109 bits)

k = 2[SUP]4[/SUP] × 3[SUP]4[/SUP] × 5 × 37 × 167 × 197 × 1459 × 3637 × 6703 × 492629

 VictordeHolland 2015-03-12 11:14

B-S is working great for me this year:
[code][Thu Mar 12 01:00:38 2015]
P-1 found a factor in stage #2, B1=10000000, B2=200000000, E=12.
UID: VictordeHollander/PCVICTOR, M1545007 has a factor: 9694966038406498466146561 (P-1, B1=10000000, B2=200000000, E=12)[/code]k = 3137515246988039040 = 27 × 3 × 5 × 17 × 42,181 × 2,278,866,181
25 digits 83.004 bits

2,278,866,181 > 11x B2(200,000,000)!

 VictordeHolland 2015-03-18 11:17

My 4th B-S this year!

[code]P-1 found a factor in stage #2, B1=10000000, B2=200000000, E=12.
UID: VictordeHollander/PCVICTOR, M1526977 has a factor: 22259470830172378348329617 (P-1, B1=10000000, B2=200000000, E=12)[/code]26 digits 84.203 bits
k = 7288738085174949704 = 23 × 73 × 71 × 15,161 × [B]2,467,641,361[/B]
2,467,641,361 >12 x B2(200,000,000)

 LaurV 2015-03-18 11:57

Lucky son of a gun! Congrats!
I have only 3 or 4 Brent-Suyama hits in lifetime (if I am not mistaken, one was from Kracker's computers, when we were exchanging GHzDays).

 legendarymudkip 2015-03-27 16:35

M50273 has a factor: 987139826417276834314931283761815154689 (129.537 bits)
k = 2[SUP]11[/SUP] × 3[SUP]3[/SUP] × 53 × 3349996012462457805367581481 (I hope you have plenty of memory for stage 2 :razz:)
Sigma 309170328303138 gave group order 2[SUP]6[/SUP] · 3[SUP]2[/SUP] · 103 · 599 · 1373 · 2129 · 2311 · 6091 · 159793 · 252359 · 16740979, could've been found with t30 bounds instead of t40, but wrong sigmas tested, you can never know.

 lycorn 2015-03-27 19:18

Congrats! It was a juicy one...

 firejuggler 2015-04-03 08:36

first factor in a while.
M36794633 has a factor: 7547690687957650291279 (found by P-1,72.677 bits))
k=3*7*37*47*523*5370059
Would it have been faster with a B1 of 5370060 or with a B1 @523 and a B2@5370060?

 VBCurtis 2015-04-03 15:57

[QUOTE=firejuggler;399275]first factor in a while.
M36794633 has a factor: 7547690687957650291279 (found by P-1,72.677 bits))
k=3*7*37*47*523*5370059
Would it have been faster with a B1 of 5370060 or with a B1 @523 and a B2@5370060?[/QUOTE]

I'm pretty sure B2 cannot exceed the square of B1. This is true for ECM, at least.

 axn 2015-04-03 16:01

[QUOTE=VBCurtis;399289]I'm pretty sure B2 cannot exceed the square of B1. This is true for ECM, at least.[/QUOTE]

I don't understand this statement. Why can't B2 exceed square of B1 (for both P-1 and ECM)?

 R.D. Silverman 2015-04-03 20:47

[QUOTE=VBCurtis;399289]I'm pretty sure B2 cannot exceed the square of B1. This is true for ECM, at least.[/QUOTE]

False for both. Why don't you try learning how both algorithms work before making future
pronouncements?

 VBCurtis 2015-04-03 21:16

[QUOTE=axn;399290]I don't understand this statement. Why can't B2 exceed square of B1 (for both P-1 and ECM)?[/QUOTE]

I think you do understand the statement- it's just that it's incorrect. I went back and skimmed both the Silverman and Montgomery papers looking for support for my statement, and found nothing. Then I ran ECM with B1 = 1e5 and B2 = 1e12, and it ran fine. So, I'm simply mistaken.

I distinctly remember reading about this relationship... I'll keep looking, but perhaps I am only recalling a claim that B2 > B1^2 is always suboptimal; that is, to find a factor most quickly, B2 should be selected to be less than the square of B1.

So, very incorrect statement, but that's where my poor B1^2 recollection came from.

 LaurV 2015-04-04 03:42

Actually, for example for P-1, you do powering in stage 1 to compute b^E, which you store. Then in stage 2 you "add" more primes to this powering with a single multiplication. You compute something like b^(E*R) for different R=product of k primes*. The trick is that you can test more primes (as possible factors of q-1, where q is the factor you try to find) with a single multiplication. That is why you can extend stage 2 (B2) higher. As you waste about the same time to do a squaring as you waste to do a multiplication, the right cutting point should be something like B2=k*B1^2, where k is the number of primes in R.

Well, this ignores a lot of other things, like for example, the prime numbers have a... cheesy distribution, you pick one prime q by random, what is the probability that q-1 has all factors lower than B1 except exactly one factor which is higher? How many (even) numbers (in percent) of an indicated size are product of only a big prime and some small prime? etc...

------
*yeah, I know you take some "constellation" only, which also will contain non-primes, this is not the point here

 VictordeHolland 2015-04-13 20:34

My P-1 runs in the 1.5M range (with B1=10M, B2=200M) are finding a lot of factors with the Brent-Suyama extention:
[code][Sun Apr 12 00:16:52 2015]
P-1 found a factor in stage #2, B1=10000000, B2=200000000, E=12.
UID: VictordeHollander/PCVICTOR, M1567483 has a factor: 10229405036637564504977 (P-1, B1=10000000, B2=200000000, E=12)
[/code]k = 3263003501995736 = 2^3 × 29 × 28027 × [B]501,825,749[/B]
23 digits 73.115 bits

And a day later another one!
[code]
[Mon Apr 13 11:35:49 2015]
P-1 found a factor in stage #2, B1=10000000, B2=200000000, E=12.
UID: VictordeHollander/PCVICTOR, M1584157 has a factor: 6061174682472739845780233437247 (P-1, B1=10000000, B2=200000000, E=12)[/code]k = 1913059968952805765394539 = 137 × 60943 × 9,442,729 × [B]24,265,355,701[/B]
31 digits 102.257 bits

 Jwb52z 2015-04-21 14:16

P-1 found a factor in stage #1, B1=700000.
UID: Jwb52z/Clay, M77025833 has a factor: 36815836598984416959313 (P-1, B1=700000),

I haven't been able to do P-1 in over a year until the last few days, so I was very pleased to find a factor again.

 lycorn 2015-04-21 14:25

Welcome back! :smile:

 firejuggler 2015-04-21 20:38

P-1 found a factor in stage #2, B1=670000, B2=12730000.
UID: firejuggler, M76039529 has a factor: 27414116836656177011399 (74.537 bits)
k=7^2 × 344237 × 10686887

 Jwb52z 2015-04-21 22:32

Thank you. :) I was looking back at some of my past found factors and I can't for the life of me remember how I figured out or obtained the bits for the factors.

 firejuggler 2015-04-21 22:34

log(factor)/log(2)

 Jwb52z 2015-04-21 23:30

I didn't remember having to do math to figure it out and then I found a saved URL to a page on the Mersenne website, but it no longer works. It was at: [url]http://mersenne-aries.sili.net/exponent.php?exponentdetails=[/url]

I wonder if it's another page now or if there is no page like this now. If I remember correctly, it figured out the bits for you when you input the factor found.

 firejuggler 2015-04-21 23:38

[url]http://www.mersenne.ca/[/url] lower right box

 Jwb52z 2015-04-21 23:38

Thank you! :) I can't edit that post anymore, so I'll just put it here: 74.963 bits

 Jwb52z 2015-04-29 01:45

UID: Jwb52z/Clay, M76106587 has a factor: 2253706211548544927116376383 (P-1, B1=690000, B2=12937500)

90.864 bits

 Jwb52z 2015-05-10 14:01

P-1 found a factor in stage #2, B1=715000, B2=13227500.
UID: Jwb52z/Clay, M78208159 has a factor: 5980644118600514360767129 (P-1, B1=715000, B2=13227500)

82.307 bits

 Jwb52z 2015-05-15 01:54

P-1 found a factor in stage #2, B1=690000, B2=12937500.
UID: Jwb52z/Clay, M76097309 has a factor: 160406892606660651307306068007 (P-1, B1=690000, B2=12937500)

97.018 bits.

 tha 2015-05-18 20:54

I found a factor for the [URL="http://www.mersenne.ca/exponent/12973951"] exponent 12973951[/URL] which has 2^11 as part of the value for 'k'. Any exponent with a 'k' that includes a higher power than 11?

 TheJudger 2015-05-18 22:30

Hi tha,

you've asked for it, perhaps my highscore:[LIST][*][url]http://www.mersenne.ca/exponent/62419603[/url][/LIST]and some slightly lower powers of 2:[LIST][*][url]http://www.mersenne.ca/exponent/70213463[/url][*][url]http://www.mersenne.ca/exponent/60967087[/url][*][url]http://www.mersenne.ca/exponent/65490281[/url][*][url]http://www.mersenne.ca/exponent/72541463[/url][/LIST]
and some even lower powers of 3:[LIST][*][url]http://www.mersenne.ca/exponent/66150701[/url][*][url]http://www.mersenne.ca/exponent/59890121[/url][*][url]http://www.mersenne.ca/exponent/71694323[/url][/LIST]
and for 5:[LIST][*][url]http://www.mersenne.ca/exponent/68938921[/url][/LIST]
Oliver

 LaurV 2015-05-19 06:07

If p is 1 (mod 4), then k can be 0 or 3 (mod 4), and if p is 3 (mod 4), then k can be 0 or 1 (mod 4). There is no k which is 2 (mod 4) because in this case 2kp+1 would be either 3 or 5 (mod 8) which is not possible for a factor.

Therefore, considering that 50% of the factors have a k which is 0 (mod 4), (i.e. 50% of the k's are multiple of 2^2 already) then about one in 1000 will have a k which is 0 (mod 2^11). As we have few millions of them...

 TObject 2015-05-26 22:02

Nice couple of factors for an exponent

[b]M78098261[/b] has a factor q=2715126139938490881846927116066757839; log2(q)=[b]121.03...[/b]
k = 11*13*3911*7321*81547*1802039*28890311 = 17382756704009650623635058379; log2(k)=93.812...

[b]M78098261[/b] has a factor q=56873105138451031651367; log2(q)=[b]75.59...[/b]
k = 19 * 23^2 * 29 * 163 * 7663739 = 364112493736903; log2(k)=48.371...

 TheJudger 2015-05-27 21:25

indeed not a every day factor, congratulations!

Oliver

P.S. I know there is nothing specials about these factors, small or big, B1-smooth or not, a factor is a factor. But bigger factors feel better than smaller ones (bigger is better!).

 Gordon 2015-05-28 21:27

[QUOTE=TObject;403018][b]M78098261[/b] has a factor q=2715126139938490881846927116066757839; log2(q)=[b]121.03...[/b]
k = 11*13*3911*7321*81547*1802039*28890311 = 17382756704009650623635058379; log2(k)=93.812...

[b]M78098261[/b] has a factor q=56873105138451031651367; log2(q)=[b]75.59...[/b]
k = 19 * 23^2 * 29 * 163 * 7663739 = 364112493736903; log2(k)=48.371...[/QUOTE]

Which leads to the interesting thought, if we had run TF to 76 bits and found the factor, how long would it have been before we found the 121 bit one...

 TObject 2015-05-28 22:53

True.

Also, with slightly higher B1, the 76-bit factor could have shown up in the Stage 1 and the Stage 2 would not run at all.

 Jwb52z 2015-06-01 02:04

P-1 found a factor in stage #2, B1=700000, B2=12950000.
UID: Jwb52z/Clay, M77149753 has a factor: 100126154465201540478799 (P-1, B1=700000, B2=12950000)

76.406 bits.

 lycorn 2015-06-01 19:57

Another one down:

UID: lycorn/asteroid, M27943 has a factor: 9595745432621621468883227471666940222487 (ECM curve 228, B1=3000000, B2=300000000),

132.818 bits

k = 3 × 7 × 2029 × 20873 × 575231 × 47418037 × 7077886967119

Not too rough, not too smooth. Just fine... :smile:

 aurashift 2015-06-01 23:21

I keep seeing this thread on my way into LMH>100M

[url]http://www.mersenne.ca/exponent/78282691[/url]

127 bits, do i win a prize?

 firejuggler 2015-06-01 23:39

thats a really nice factor

 PageFault 2015-06-04 03:06

Nice find!

Are you going to do your others to B1=44000000? I did a test on my block, M25xxx, and got 27 curves per day. Quite an effort, to finish these 10 or so through to 17100 curves, several years or so ... I'll begin mass deployment in a few days time, is it better to do chunks of each on all cores or the full run on a single core? The latter will take over a year ...

I hope they come up with better hardware real soon, and that I can be positioned to make advantage ... long stretch needless to say, but I am determined. Am I crazy enough to finish this, and embark on the next B1 ???

BTW Stage 2 only takes 750 MB.

[QUOTE=lycorn;403360]Another one down:

UID: lycorn/asteroid, M27943 has a factor: 9595745432621621468883227471666940222487 (ECM curve 228, B1=3000000, B2=300000000),

132.818 bits

k = 3 × 7 × 2029 × 20873 × 575231 × 47418037 × 7077886967119

Not too rough, not too smooth. Just fine... :smile:[/QUOTE]

 alpertron 2015-06-04 11:31

Today my computer found a prime factor of the same size (133 bits):

[Thu Jun 04 02:54:08 2015]
P-1 found a factor in stage #2, B1=1000000, B2=30000000, E=12.
M955363 has a factor: 7315800908340060929629104157850801671121 (P-1, B1=1000000, B2=30000000, E=12)

k = 2^3 × 5 × 173 × 3733 × 4111 × 100361 × 102563 × 298631 × 11729009

 lycorn 2015-06-04 23:06

[QUOTE=PageFault;403471]Nice find!

Are you going to do your others to B1=44000000? I did a test on my block, M25xxx, and got 27 curves per day. Quite an effort, to finish these 10 or so through to 17100 curves, several years or so ... I'll begin mass deployment in a few days time, is it better to do chunks of each on all cores or the full run on a single core? The latter will take over a year ...

I hope they come up with better hardware real soon, and that I can be positioned to make advantage ... long stretch needless to say, but I am determined. Am I crazy enough to finish this, and embark on the next B1 ???

BTW Stage 2 only takes 750 MB.[/QUOTE]

I will do several tests with B1=11e6 for the next couple of months (exponents ranging from 12000 to 15000).
I will also pursue the quest for a factor of M1277, using Prime95 for Stage 1 and GMP-ECM for Stage 2. If you have a fair amount of memory available, you could also give it a go.

As for how to split the tests among several cores, there´s not a lot to be gained in doing it one way or the other. If I were you, I would probably do a mix: e.g. test 2 exponents on 4 cores, assigning 2 chunks of the same test to each core. That´s what I´m currently doing...

 firejuggler 2015-06-05 01:30

a nice one down pm1 find
M78235639 has a factor 8803993906198449472411631 (82.6 bit, ) found in stage 1
k=5 × 43 × 131 × 3643 × 5827 × 94109

[QUOTE=lycorn;403523]I will also pursue the quest for a factor of M1277, using Prime95 for Stage 1 and GMP-ECM for Stage 2. If you have a fair amount of memory available, you could also give it a go.[/QUOTE]

I'm about halfway through doing P-1 on M1277 at:
B1=5,000,000,000,000 B2=10,000,000,000,000

Methinks it'll finish in a couple more weeks or something. I was bored and thought it'd be fun to allocate a few spare cores to P-1 work on smaller exponents, even though I know ECM would probably be more fruitful, or so I've heard.

I'm also doing these to the same bounds:
M1619
M1753
M2137
M2267
M2273

Each running on one core of a 6-core Xeon (while the other chip in this dual-CPU system is doing LL tests).

I started the M1277 run a while back so it's further along. The other ones will be a month or so before finishing up. Those last two are only at 14% right now.

Speaking of P-1, is there any consensus out there about the fastest program for P-1 work? Would gmp-ecm be something to look at for P-1 as well as ECM, or maybe something else (Windows based)?

 lorgix 2015-06-06 10:54

B1=5,000,000,000,000 B2=10,000,000,000,000

Methinks it'll finish in a couple more weeks or something. I was bored and thought it'd be fun to allocate a few spare cores to P-1 work on smaller exponents, even though I know ECM would probably be more fruitful, or so I've heard.

I'm also doing these to the same bounds:
M1619
M1753
M2137
M2267
M2273

Each running on one core of a 6-core Xeon (while the other chip in this dual-CPU system is doing LL tests).

I started the M1277 run a while back so it's further along. The other ones will be a month or so before finishing up. Those last two are only at 14% right now.

Speaking of P-1, is there any consensus out there about the fastest program for P-1 work? Would gmp-ecm be something to look at for P-1 as well as ECM, or maybe something else (Windows based)?[/QUOTE]
If you are doing stage1 all the way to 5e12 it's highly recommended that you take stage2 further than 1e13. Maybe 6e13~1e14 or so.

Yes, ECM is more efficient.

For large enough numbers Prime95 is faster in stage1. GMP-ECM is faster in stage2, depending on bounds and input size.
So in short; it depends. But GMP-ECM can be way faster in stage2.

 LaurV 2015-06-07 16:13

For how much ECM was done on these thingies, there is a [U]very[/U] slim chance that P-1 finds a factor.

 lycorn 2015-06-07 19:46

Yeah, Prime95+GMP-ECM would really be the best bet for the lowest exponents in Primenet ranges, specially for machines with large amounts of memory.

[QUOTE=LaurV;403638]For how much ECM was done on these thingies, there is a [U]very[/U] slim chance that P-1 finds a factor.[/QUOTE]

Yeah, that could very well be true, I was just goofing around with the P-1 stuff and thought I'd see, just push it a little past where it was.

I'd done some ECM on M1277 previously and I may return to that once I tidy up this triple-checking... I'm still a little dissatisfied with the complexity of using Prime95 for stage 1 and GMP-ECM for stage 2, and all that goes into that, but oh well, if that's not a first world problem, I don't know what is. :smile:

 TheJudger 2015-06-07 20:34

no a big one... but smooooooooooooooth :smile:

P-1 found a factor in stage #1, B1=685,000.
M74,149,633 has a factor: 54,782,821,866,922,527,235,217 (75.53 Bits)
k = 369,407,235,413,576 = 2[SUP]3[/SUP] * 31 * 53 * 163 * 433 * 491 * 811

Oliver

 LaurV 2015-06-08 05:55

[QUOTE=Madpoo;403648]I was just goofing around with the P-1 stuff and thought I'd see, just push it a little past where it was[/QUOTE]
Man, I am not criticizing, just stating a fact. Don't forget that I was the "silly" who did that huge P-1 for M1061. You never know where the luck stays crouching... hehe...

 lycorn 2015-06-18 07:38

A giant factor (421 bits) for M991 was reported a couple of hours ago by George Woltman.
I wonder how it was found...

 axn 2015-06-18 09:41

[QUOTE=lycorn;404322]A giant factor (421 bits) for M991 was reported a couple of hours ago by George Woltman.
I wonder how it was found...[/QUOTE]

 lycorn 2015-06-18 11:45

Thx.

 Dubslow 2015-06-18 14:48

 alpertron 2015-06-27 00:53

P-1 found a factor in stage #2, B1=1000000, B2=30000000, E=12.
M974329 has a factor: 713552035392139301665463340620467463 (P-1, B1=1000000, B2=30000000, E=12)

k = 47 × 727 × 887 × 1049 × 6079 × 10333 × 14071 × 13030921

 petrw1 2015-06-29 22:31

Somewhat interesting factor....

48713897 F 1111103198672818834999

 Jwb52z 2015-07-28 00:55

P-1 found a factor in stage #2, B1=620000, B2=11470000.
UID: Jwb52z/Clay, M72551777 has a factor: 62016063905814958506247

75.715 bits

 Gordon 2015-08-01 01:06

[Fri Jul 31 10:24:52 2015]
ECM found a factor in curve #1, stage #2
Sigma=1802940857370980, B1=50000, B2=5000000.
UID: nitro/haswell, M10747343 has a factor: 7860697152906126698999041 (ECM curve 1, B1=50000, B2=5000000), AID: D9BFB39C3F0944893BACD085A53******

[URL="http://www.mersenne.ca/exponent/10747343"]82.7 bits[/URL]

74,000 days to do TF on :exclaim:

 Jwb52z 2015-08-07 04:32

P-1 found a factor in stage #1, B1=615000.
UID: Jwb52z/Clay, M72162049 has a factor: 163517881312940080765049 (P-1, B1=615000)

77.114 bits.

 Jwb52z 2015-08-13 00:53

P-1 found a factor in stage #2, B1=670000, B2=12730000.
UID: Jwb52z/Clay, M77151071 has a factor: 105112265729878315512607 (P-1, B1=670000, B2=12730000)

76.476 bits.

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