Nice find :tu:

P1 found a factor in stage #1, B1=640000.
UID: Jwb52z/Clay, M74822911 has a factor: 246259810267427297611010947961 (P1, B1=640000) 97.636 bits. 
Every time I see a new post here I'm hoping it is a factor of M1277 or M1619, even tough I know it is very unlikely :razz:

[QUOTE=Jwb52z;418258]P1 found a factor in stage #2, B1=645000, B2=12255000.
UID: Jwb52z/Clay, M75143573 has a factor: 2223935088334736540260164531842793066322489490183317406066993 (P1, B1=645000, B2=12255000) It's a composite factor according to Prime95, but the results file doesn't save the 2 parts that this factor becomes, so I don't know how to post them to this message.[/QUOTE] You can see both prime factors at: [url]http://www.mersenne.org/report_exponent/?exp_lo=75143573&exp_hi=[/url] 
P1 found a factor in stage #2, B1=635000, B2=11906250.
UID: Jwb52z/Clay, M74476733 has a factor: 336605492262437911582967 (P1, B1=635000, B2=11906250) 78.115 bits. 
[Fri Dec 18 10:17:33 2015]
P1 found a factor in stage #2, B1=885000, B2=23231250, E=6. UID: firejuggler, M79022257 has a factor: 229423566425068458592273046541231647814785995393 (P1, B1=885000, B2=23231250, E=6), (157 bits) it is composite of course,229423566425068458592273046541231647814785995393 =38679971773795566333239 (75 bits) * 5931327141776652671572487 (82.3 bits) 
201667  factored
It has a 91 bit factor
[Sun Jan 24 08:10:30 2016] ECM found a factor in curve #112, stage #2 Sigma=8829084939581650, B1=250000, B2=30000000. M201667 has a factor: 2073051546873901675394238319 (ECM curve 112, B1=250000, B2=30000000) 
M137395267 has a factor: 299720439373335925337 [TF:68:69:mfaktc 0.21 barrett76_mul32_gs]
found 1 factor for M137395267 from 2^68 to 2^69 [mfaktc 0.21 barrett76_mul32_gs] [I]my first find! 68 bits[/I] M78914653 has a factor: 3946892419366218369503 [TF:71:72:mfaktc 0.21 barrett76_mul32_gs] found 1 factor for M137395267 from 2^71 to 2^72 [mfaktc 0.21 barrett76_mul32_gs] 
[QUOTE=christianpoland;425739][I]my first find! 68 bits[/I]
[/QUOTE] Welcome to the club. We understand your enthusiasm, and we like it :smile:, but first, you don't need to post every (small) factor you find, and second, technically, that number has 69 bits :razz: Again, welcome to the fray! 
M146059
Not mine unfortunately, I logged in factoring results for numbers in the 140k range and got a result not needed for the above, this is the reason why
20160215 kadir emir Factor: 12663133710644208611823239476283651826271 133 bits.... 
P1 found a factor in stage #2, B1=645000, B2=12416250.
UID: Jwb52z/Clay, M77321767 has a factor: 63410308039841666453639 (P1, B1=645000, B2=12416250) 75.747 bits. 
[Sun Feb 21 20:33:02 2016]
P1 found a factor in stage #[B]1[/B], B1=300000. UID: Tha/DellCore2_3GHz, [URL="http://www.mersenne.org/report_exponent/?exp_lo=15826841&full=1"]M15826841[/URL] has a factor: 1557959868912222903757721123389359001 (P1, B1=300000) k = 2[SUP]2[/SUP]×3×5[SUP]3[/SUP]×37×6 907×12 899×135 353×265 739×276 739 121 bits (120,2) 
Impressive!

P1 found a factor in stage #2, B1=645000, B2=12416250.
UID: Jwb52z/Clay, M77349803 has a factor: 1073144601225330493391839 (P1, B1=645000, B2=12416250) 79.828 bits. 
M30253 falls...
It has a 122 bit factor
ECM found a factor in curve #720, stage #2 Sigma=3385722498712908, B1=3000000, B2=400000000. UID: nitro/haswell, M30253 has a factor: 4369956377031302093316331957913567537 (ECM curve 720, B1=3000000, B2=400000000) Total number of curves run was 1621 
Wow, lucky you!
I´ve been digging in that range as well, but so far so... bad. :bangheadonwall: 
[QUOTE=lycorn;427330]Wow, lucky you!
I´ve been digging in that range as well, but so far so... bad. :bangheadonwall:[/QUOTE] Sometimes you just get lucky! It's the smallest exponent I've factored beating out 32029 Everything from 2880730161 is now tested up to T40 and I have 3 stage 1's running at the present all for T40 testing 30169  2500 curves 30187  2500 curves 30223  2000 curves 
Ah, that´s funny. I just had a look at the work I have queued and 30253 was actually due to start tomorrow or so. It´s also a good thing that you´ve posted the ones you´ve running, for 30223 is also in my queue. Oh well, time to get rid of them and get some fresh ones...
BTW, the smallest exp I ever factored is 20011 (B1 bound 11M). :razz: 
[QUOTE=lycorn;427332]Ah, that´s funny. I just had a look at the work I have queued and 30253 was actually due to start tomorrow or so. It´s also a good thing that you´ve posted the ones you´ve running, for 30223 is also in my queue. Oh well, time to get rid of them and get some fresh ones...
BTW, the smallest exp I ever factored is 20011 (B1 bound 11M). :razz:[/QUOTE] They are all 1650 curves in, have just started 1000 curves on 30431, I ran quite a few curves in 16k17k range but nothing so far, maybe the next one :tu: 
Just so you know, I´ve already run over 3800 curves on 30491, and will finish the run tomorrow evening, completing the prescribed number of curves for a 3M B1 bound. You´ll probably wish to stay away from that one...

Just a warning, to avoid doublework. For a week now, I am running curves (B1=3000000) on the following: M33037, M33091, M33151, M38197. I aim of completing the bitlevel, so it might take some more weeks. So far about 500 curves on all 33...s and 1200 curves on 38...

[QUOTE=bloodIce;427390]Just a warning, to avoid doublework. For a week now, I am running curves (B1=3000000) on the following: M33037, M33091, M33151, M38197. I aim of completing the bitlevel, so it might take some more weeks. So far about 500 curves on all 33...s and 1200 curves on 38...[/QUOTE]
ECM work is not really duplicated or wasted. 
[QUOTE=axn;427393]ECM work is not really duplicated or wasted.[/QUOTE]
True, but a record of who has done how much work where is never a bad thing. 
What are the chances two people will run exactly the same curve? Extremely small?

I decided to take a punt on an exponent I had been assigned:
no factor for M77961971 from 2^75 to 2^76 [mfaktc 0.21 barrett76_mul32_gs] no factor for M77961971 from 2^76 to 2^77 [mfaktc 0.21 barrett87_mul32_gs] no factor for M77961971 from 2^77 to 2^78 [mfaktc 0.21 barrett87_mul32_gs] M77961971 has a factor: 533579269373988895703777 took me over 1000GHz days of work :) [url]http://www.mersenne.ca/exponent/77961971[/url] I was thankful that that isn't easily found by P1 though, didn't want to think I'd wasted my GPU cycles! I know it's not the largest factor on here but it's probably the one I've spent the most time on and actually succeeded :) 
Good find. I also take wave front first time exponents to 79 before assigning them to really old machines… For newer computers it makes sense to just run the LL test.

P1 found a factor in stage #1, B1=615000.
UID: Jwb52z/Clay, M74683031 has a factor: 44664350248380904476819193 (P1, B1=615000) 85.207 bits. 
P1 found a factor in stage #1, B1=630000.
UID: Jwb52z/Clay, M75909133 has a factor: 1460917115983359723544993 (P1, B1=630000) 80.273 bits. 
Another one bites the dust:
ECM found a factor in curve #216, stage #2 Sigma=6254442244963386, B1=11000000, B2=1100000000. UID: lycorn/asteroid,[B] M15149 has a factor[/B]: 3519184049073327944797207886908866406374551 (ECM curve 216, B1=11000000, B2=1100000000), 141.336 bits, and prime. It´s the lowest number I ever factored. Broke my previous record of M20011. 
[QUOTE=lycorn;429221]Another one bites the dust:
ECM found a factor in curve #216, stage #2 Sigma=6254442244963386, B1=11000000, B2=1100000000. UID: lycorn/asteroid,[B] M15149 has a factor[/B]: 3519184049073327944797207886908866406374551 (ECM curve 216, B1=11000000, B2=1100000000), 141.336 bits, and prime. It´s the lowest number I ever factored. Broke my previous record of M20011.[/QUOTE] Very nice :bow: When I finish taking the 30k31k range all up to a full T40 think I might head lower... 
[QUOTE=lycorn;429221]It´s the lowest number I ever factored. Broke my previous record of M20011.[/QUOTE]
:tu: Congrats! This was a nice one! 
P1 found a factor in stage #1, B1=625000.
UID: Jwb52z/Clay, M75565537 has a factor: 148893459288809851942730148146257 (P1, B1=625000), 106.876 bits. 
[QUOTE=Jwb52z;430053]P1 found a factor in stage #1, B1=625000.
UID: Jwb52z/Clay, M75565537 has a factor: 148893459288809851942730148146257 (P1, B1=625000), 106.876 bits.[/QUOTE] Any factor above 100 bits is a nice find :smile: 
M79868531 has a factor: 10101962748952461002670427757775497 (P1, B1=925000, B2=23125000, E=6)
112.96 bits M36850673 has a factor: 2693201601654787419167 [TF:71:72*:mfaktc 0.21 barrett76_mul32_gs] 71.18 bits 
P1 found a factor in stage #2, B1=625000, B2=11718750.
UID: Jwb52z/Clay, M75794029 has a factor: 43982252594175718118846617 (P1, B1=625000, B2=11718750) 85.185 bits. 
Most of the ones I find tend to be between 75 and 90.

Hi, long time since last post in this thread from myself:
P1 found a factor in stage #2, B1=665,000, [B][COLOR="Red"]B2=13,300,000[/COLOR][/B], E=12. M76,642,547 has a factor: 1,103,265,758,603,666,759,577,767 (79.86 Bits; k = 7,197,475,826,342,689 = 19 * 233,329 * [B][COLOR="Red"]1,623,520,939[/COLOR][/B]) Oliver 
Wow, on the scale of smooth to chunky that's definitely an outlier.

M35210753 has a factor: 10176353483612315371063 [TF:73:74*:mfakto 0.14MGW cl_barrett15_82_gs_2]
73.107 bits 
P1 found a factor in stage #2, B1=625000, B2=11718750.
UID: Jwb52z/Clay, M75754391 has a factor: 273367018208176123158583 (P1, B1=625000, B2=11718750), Unfortunately, right now as I type this, the site for figuring the bit depth of the factor is down or not reachable for me. 
[QUOTE=Jwb52z;432283]P1 found a factor in stage #2, B1=625000, B2=11718750.
UID: Jwb52z/Clay, M75754391 has a factor: 273367018208176123158583 (P1, B1=625000, B2=11718750), Unfortunately, right now as I type this, the site for figuring the bit depth of the factor is down or not reachable for me.[/QUOTE]log(273367018208176123158583)/log(2) = 77.855... 
[QUOTE=retina;432288]log(273367018208176123158583)/log(2) = 77.855...[/QUOTE]
Thank you. I do appreciate you finding/calculating that for me. The site is back up right now, so I hope I won't have this problem again any time soon. 
[QUOTE=Jwb52z;432386]Thank you. I do appreciate you finding/calculating that for me. The site is back up right now, so I hope I won't have this problem again any time soon.[/QUOTE]If your system has a calculator application then you can compute it without the need to rely on an external website.
[size=1]For simple stuff like this we shouldn't really be relying on the "cloud" to do it for us, we have computers in front of us ready and waiting to do this kind of thing. And it would take a lot less cycles than using a browser and network connection, so it would leave more cycles for finding more factors.[/size] 
M332291837 1435427839904569127627303
80.248 bits [url]http://www.mersenne.ca/exponent/332291837[/url] 
[QUOTE=retina;432391]If your system has a calculator application then you can compute it without the need to rely on an external website.
[/QUOTE] Just be careful with something like Microsoft Excel, because it will silently cut down the precision to whatever is the maximum it can work with. There is xNumbers library that adds arbitrary precision functions to Excel. 
Small One Turns Up A Large One
ECM found a factor in curve #54, stage #2
Sigma=6792843557510917, B1=1000000, B2=100000000. M90679 has a factor: 6589076784209827854482269064939889241 (ECM curve 54, B1=1000000, B2=100000000) 122.3 bits.... 
Good one. It's always nice to knock out a sub100k...

Yep, a good one. You found it four days after my ECM on the exponent, so I had my chance, but did not score. Great, one more is down.

another sub100K bites the dust
[Mon Jun 6 23:12:20 2016]
ECM found a factor in curve #218, stage #2 Sigma=3267888520893954, B1=3000000, B2=300000000. UID: BloodIce/URM2, M40423 has a factor: 164989575420758840709086391456486169 [URL]http://www.mersenne.ca/exponent/40423[/URL] : ~117 bits 
[QUOTE=bloodIce;435692][Mon Jun 6 23:12:20 2016]
ECM found a factor in curve #218, stage #2 Sigma=3267888520893954, B1=3000000, B2=300000000. UID: BloodIce/URM2, M40423 has a factor: 164989575420758840709086391456486169 [URL]http://www.mersenne.ca/exponent/40423[/URL] : ~117 bits[/QUOTE] Even better, a sub 50k exponent goes down...:smile: 
And another one...
@bloodice: you're getting really good at finding these...
How do you do it? :smile: M36109 has a factor. 
[QUOTE=lycorn;435743]@bloodice: you're getting really good at finding these...
How do you do it? :smile: M36109 has a factor.[/QUOTE] Put us out of our misery then... :smile: 
sub40K down today
Today a sub40K bites the dust:
[Tue Jun 7 22:10:49 2016] ECM found a factor in curve #113, stage #1 Sigma=629186646856962, B1=3000000, B2=300000000. UID: BloodIce/Mjolnir4, M36109 has a factor: 600691002840126002796941760359632040567 (ECM curve 113, B1=3000000, B2=300000000) [URL]http://www.mersenne.ca/exponent/36109[/URL]: ~129 bits P.S.: Hehe, thanks for the friendly support. No mystery, just dedicating 7 cores for small ECM work and of course try 3 to 4 neighbouring exponents in batches on each machine. It is an extreme luck, that is what it is :). 
[code]
ECM found a factor in curve #196, stage #2 Sigma=7609780438895502, B1=50000, B2=5000000. UID: VictordeHollander/PC3770K, M1557419 has a factor: 2913347056784507060325933694843071809 (ECM curve 196, B1=50000, B2=5000000)[/code] Not very special in terms of size (37 digits, 122 bits), but pretty decent hit with only B1=50,000 and B2=5,000,000 
M5923 factored
Congratulations to Carsten Kossendey.

Indeed.
That one was a real teaser... I've been squeezing M5879 hard, but to no avail. In a week or so B1=44000000 will be fully tried. 
P1 found a factor in stage #1, B1=660000.
UID: Jwb52z/Clay, M78647759 has a factor: 479779549412952847946157679 (P1, B1=660000) 88.633 bits. 
[QUOTE=Jwb52z;436491]P1 found a factor in stage #1, B1=660000.
UID: Jwb52z/Clay, M78647759 has a factor: 479779549412952847946157679 (P1, B1=660000) 88.633 bits.[/QUOTE] Nice find, a lot of time saved for the project :smile: 
two sub40K down
[Fri Jun 24 20:28:53 2016]
ECM found a factor in curve #203, stage #1 Sigma=61541048953985, B1=3000000, B2=300000000. UID: BloodIce/Mjolnir4, M35591 has a factor: 137728575725419534448289970535976313 (ECM curve 203, B1=3000000, B2=300000000) ~117 bits [Sat Jun 25 05:40:14 2016] ECM found a factor in curve #576, stage #2 Sigma=7459404930796059, B1=3000000, B2=300000000. UID: BloodIce/Mjolnir4, M35537 has a factor: 1532578067845635137525157423375548167 (ECM curve 576, B1=3000000, B2=300000000) ~120 bits It seems to be very hard to find factors on sub20K exponents, but in 30K range they are plenty of exponents which could be factored. 
whoaa! nice! congrats!
Anyone does PRP tests for the two? 
I have checked the remaining cofactors of course (among the first thing I do after a factor in the lower range). Or do you mean PRP of the factors? I hope mersenne.org has a code to deal with the factors once they arrive.

34537 is down
[Sat Jul 2 02:44:21 2016]
ECM found a factor in curve #1191, stage #2 Sigma=8753620462425117, B1=3000000, B2=300000000. UID: BloodIce/Mjolnir4, M34537 has a factor: 442299498283919300728290218941317553933121 (ECM curve 1191, B1=3000000, B2=300000000) ~138 bits, the cofactor is not prime. 
[QUOTE=bloodIce;437015]I have checked the remaining cofactors of course (among the first thing I do after a factor in the lower range). Or do you mean PRP of the factors? I hope mersenne.org has a code to deal with the factors once they arrive.[/QUOTE]
PRP of the remaining cofactor. Mersenne.org verifies reported factors for primality (amoungst other things). I believe James site also does PRP test on sub 1M exponents after new factors have been reported. 
[QUOTE=bloodIce;437400][Sat Jul 2 02:44:21 2016]
ECM found a factor in curve #1191, stage #2 Sigma=8753620462425117, B1=3000000, B2=300000000. UID: BloodIce/Mjolnir4, M34537 has a factor: 442299498283919300728290218941317553933121 (ECM curve 1191, B1=3000000, B2=300000000) ~138 bits, the cofactor is not prime.[/QUOTE] I did 400 curves on this just before Xmas, shame they were the wrong 400 :smile: 
[QUOTE=Gordon;437495]I did 400 curves on this just before Xmas, shame they were the wrong 400 :smile:[/QUOTE]
Remember M90679, we are even :smile:. But, if you wish take any of "mine exponents" and find a factor, I will only be happy. Cheers and keep the factors coming. 
[QUOTE=Gordon;436501]Nice find, a lot of time saved for the project :smile:[/QUOTE]
Thank you, and here's another I just found on my screen: P1 found a factor in stage #1, B1=660000. UID: Jwb52z/Clay, M78866311 has a factor: 122507948640290214554639 (P1, B1=660000) 76.697 bits. 
3607 is down
I thought that sub 10K are impossible to factor, but here it is:
"M3607 has a factor 162160065980366340636967897279169391509046358190713" (~167 bits). Unfortunately, the cofactor is not PRP :smile:. 
Great shot!
Funny enough, in the "history" section of the report, there´s no reference to the bounds used nor the number of curves run. Did you use a B1=1.1e8? 
[QUOTE=lycorn;438666]Great shot!
Funny enough, in the "history" section of the report, there´s no reference to the bounds used nor the number of curves run. Did you use a B1=1.1e8?[/QUOTE] Stock bounds for sure (B1=1.1e8). I do not have access to the machine right now (to pull out the log), but it is probably couple of thousand curves. 
[QUOTE=bloodIce;438665]I thought that sub 10K are impossible to factor, but here it is:
"M3607 has a factor 162160065980366340636967897279169391509046358190713" (~167 bits). Unfortunately, the cofactor is not PRP :smile:.[/QUOTE] Fantastic result :bow: I'm trying my luck down in the 4k range, you never know.... 
Also digging that area, just slightly higher  6 and 8k. Something is lurking up there... :rolleyes:

Nice find! You don't get those every day!

Whoaaa! Great one! 167 bits, hey don't come easy..

[QUOTE=bloodIce;438665]I thought that sub 10K are impossible to factor, but here it is:
"M3607 has a factor 162160065980366340636967897279169391509046358190713" (~167 bits). Unfortunately, the cofactor is not PRP :smile:.[/QUOTE]Undoubtedly [b]not[/b] impossible but equally undoubtedly not entirely trivial. Nice work. :bow: 
[code]
UID: UBR47K/5820Kfactoring, M1187803 has a factor: 180153864303424969999558424827024324050497 (P1, B1=2500000) [/code] [code] k = 2^5 × 7 × 17 × 83 × 149 × 2087 × 2689 × 4999 × 36343 × 1254971 × 1258511 [/code] 42 digits, 137 bits 
P1 found a factor in stage #2, B1=665000, B2=12635000.
UID: Jwb52z/Clay, M79197037 has a factor: 370961634783541317383089 (P1, B1=665000, B2=12635000) 78.269 bits. 
P1 found a factor in stage #1, B1=665000.
UID: Jwb52z/Clay, M79051543 has a factor: 299298328540123820149321 (P1, B1=665000) 77.986 bits 
M7090613
Factor: 73788858748680091871 / TF: 6667 In binary, this factor is 1000000000000000110101100000001010011110000100011010011100011011111 That's 15 zero bits after the first 1. This factor is only 0.0026 % above the limit of the previous TF search, which was 2[SUP]66[/SUP] = 73786976294838206464 PrimeNet awarded a magnificent 0.0001 GHzDays credit. 
Ha! Beautiful find!
The difference is so small that it totally confuses James' site, which probably uses \(ceil(log_2(q))\) to calculate the number of bits, and there is not enough precision, or the 64 bits php variable is used, because the size is (wrongly) displayed as 66 bits. :rofl: Anyhow, the right formula to be used should be \(floor(log_2(q))+1\), which also solves the problem when q is a whole power of 2 (for example, 2^2 has 3 bits). That should compensate for the low precision of the calculus (the difference between ceil and floor+1 is only when applied to an integer, and it always works when lower precision, because of the lower precision is done by truncation, in this case. If that is done by rounding, it will not work for numbers close to integers, but smaller than them, like 0.99999, etc). OTOH, the "k" of this factor is in class 175 of both 4620 and 420 classes, so if you used the 4620 (most probable) then you found it quite fast, after only 175/4620 = ~3% of the time, so you should not complain for the low credit given :razz: But if you used 420 classes, you were unlucky son of a gun, you wasted a lot of time for it! edit 2: [code] gp > ceil(log(q)/log(2)) %5 = 67 gp > log(q)/log(2) %6 = 66.00003680557622102416872376 gp > default(realprecision,3) gp > log(q)/log(2) %8 = 66.0 gp > default(realprecision,5) gp > log(q)/log(2) %10 = 66.000 gp > default(realprecision,7) gp > log(q)/log(2) %12 = 66.00004 gp > #binary(q) %13 = 67 [/code](here ceil is used as I know q is not a power of two; please note that pari's internal precision is never smaller than 15 decimals or so, even when you set it smaller, it is only used for printing, and not for calculus; for calculus he always uses his doubles) 
[QUOTE=LaurV;440627]OTOH, the "k" of this factor is in class 175 of both 4620 and 420 classes, so if you used the 4620 (most probable) then you found it quite fast, after only 175/4620 = ~3% of the time, so you should not complain for the low credit given :razz:[/QUOTE]
Yes, it was mfaktc with 4620 classes, it found it at class 175 and 3.9%. 
P1 found a factor in stage #2, B1=665000, B2=12635000.
UID: Jwb52z/Clay, M79221677 has a factor: 8331269112412704936246407 (P1, B1=665000, B2=12635000) 82.785 bits. 
[QUOTE=LaurV;440627]The difference is so small that it totally confuses James' site, which probably uses \(ceil(log_2(q))\) to calculate the number of bits, and there is not enough precision, or the 64 bits php variable is used, because the size is (wrongly) displayed as 66 bits. :rofl:[/QUOTE]The site displays 66.000 because it's right :razz:
The PHP code uses [i]log(floatval($factor), 2)[/i] to calculate the bitsize, and on my server it would return that as "66.000036805576", so a little less precision than what you calculated but appears to be right. The limiting factor is actually the singleprecision FLOAT column in the MySQL table that stores the factors, but since I'm only displaying 3 decimal places I figured it's plenty close enough. edit: on the [url=http://www.mersenne.ca/exponent/7090613]exponent page[/url] if you now mouseover the 3decimal displayed bit size you'll get the 12decimal moreprecise version if you're so inclined. And you'll have to CtrlF5 forcibly refresh if you have previously looked at the page since it's heavily cached. 
[QUOTE=James Heinrich;440756]The site displays 66.000 because it's right :razz:
The PHP code uses [i]log(floatval($factor), 2)[/i] to calculate the bitsize, and on my server it would return that as "66.000036805576", so a little less precision than what you calculated but appears to be right. The limiting factor is actually the singleprecision FLOAT column in the MySQL table that stores the factors, but since I'm only displaying 3 decimal places I figured it's plenty close enough. edit: on the [url=http://www.mersenne.ca/exponent/7090613]exponent page[/url] if you now mouseover the 3decimal displayed bit size you'll get the 12decimal moreprecise version if you're so inclined. And you'll have to CtrlF5 forcibly refresh if you have previously looked at the page since it's heavily cached.[/QUOTE] right but if it's base 2 log is greater than 66 then it is greater than 2^66 which actually has 67 bits to it's binary representation. 
[QUOTE=James Heinrich;440756]The site displays 66.000 because it's right :razz:[/QUOTE]
No, it is not. You didn't get my point. If you go for 3 decimals precision, then you should round them up, unless they are already integer, when you have to add 1.000 (this never happens for factors, as they are never a full power of 2). The value you currently display would give the FALSE impression that the factor is 66 bits, when in reality is 67. Therefore, truncation is wrong ("truncation" as in rounding down, or ignoring the other decimals, or floor function, and opposite to rounding up, or ceiling functions). [U][B]You should display 66.001[/B][/U], and in that case we will know is 67 bits. Everything that its fractional is smaller than 0.001 should be displayed as 0.001. But the patch with mousing over is also satisfactory. Not perfect, but satisfactory. edit: Best would be to have it rounded up, AND the patch with mouse hovering. Not all people do mouse hovering there. But if we see it is 66.001, so it is higher than 66, then we can mouse over if we want to see the real value. Never display "integers" unless they are really integers, AND unless they really represent the number of bits. Otherwise the title of the column is very misleading. Float values are ok, everybody knows that 13.123 is 14 bits. But 13.000 is 13 bits. Not 14. 
IMO, "bits" is always an integer and in this case would be 67. The data presently displayed in the column would be more properly be labelled log2(factor) and is correctly output as 66.000.
Of course "log2(factor)" is a lot of characters for a column label. So, perhaps the web page designer is allowed a little leeway in order to make a prettier web page. Maybe "bits[SUP]*[/SUP]" with a footnote explaining the mess or simply "log2" would be an alternative. 
I now display 3 decimal places, unless those 3 show up as ".000" in which case I automatically show as many as needed to have a nonzero as the last digit. In the case of [url=http://www.mersenne.ca/exponent/7090613]M7090613[/url], it now displays "66.00004". Of course the mouseover 12digit precision is still there, and I have added a red asterisk to the column header saying it's really log2(factor) and not real bits.
Does that work for everyone? 
Works to me. Note that the full decimal expansion was also shown in the graphs with the factor bounds, where is (and always was) correct, when mouseover the big dots (there, the expansion is more suggestive, due to the graphical view).
Good job James! (as usual) edit: however :razz: can you make it tooltip, i mean square corners and yellowish background, like the other columns? As opposite of "button" style, with round corners and white background, which it is now. The motivation is not only aesthetic, but the tooltips come instantly when you mouseover. The "button" you just added has a delay (lag) of about half second, which is bothersome, you have to "know" that is there, otherwise you don't wait for it and you lose it. 
Congratulations to Anton Repko, who found a (first) factor for [URL="http://www.mersenne.org/report_exponent/?exp_lo=26711&full=1"]M26711[/URL].
And also there is a fourth factor for [URL="http://www.mersenne.org/report_exponent/?exp_lo=4957&full=1"]M4957[/URL]. The cofactor is not probableprime. 
P1 found a factor in stage #1, B1=665000.
UID: Jwb52z/Clay, M79429249 has a factor: 1841618282000258891653289 (P1, B1=665000) 80.607 bits. 
M5233 /2913486798065813495660442702490836503/32101013028243569/9223417954129/93603692660420120110355562102857/994271
is a new probable prime. 
[QUOTE=GP2;443736]M5233 /[COLOR=Red] 2913486798065813495660442702490836503[/COLOR] / 32101013028243569 / 9223417954129 / 93603692660420120110355562102857 / 994271
is a new probable prime.[/QUOTE] That is an easily provable prime, it only has <1500 digits (no, I didn't make any calculus, and I didn't prove it yet, just a "first sight" mental evaluation). I know that Dario already parsed this range, and it was no PRP there, therefore it means a new factor was found. It can only be the biggest in your line. Did you find the new factor by yourself? Congratulations for the new factor, whoever found it. edit, indeed[URL="http://www.mersenne.org/report_exponent/?exp_lo=5233&exp_hi=&full=1"] this is new[/URL]. I marked in red to be easy to see and inserted some spaces into that line 
Yes, it is new. Good find! You can email to S.S.W for extension tables.
[SPOILER][URL]http://primes.utm.edu/primes/search.php?Advanced=1[/URL] (use Official Comment=Mersenne cofactor, type=all, Maximum Number of Primes = 2000) => not there[/SPOILER] [SPOILER]Also: dated [URL="http://factordb.com/index.php?id=1100000000869501428"]Sep 29[/URL] in factordb.com[/SPOILER] 
[QUOTE=LaurV;443751]That is an easily provable prime, it only has <1500 digits (no, I didn't make any calculus, and I didn't prove it yet, just a "first sight" mental evaluation).
I know that Dario already parsed this range, and it was no PRP there, therefore it means a new factor was found. It can only be the biggest in your line. Did you find the new factor by yourself? Congratulations for the new factor, whoever found it. edit, indeed[URL="http://www.mersenne.org/report_exponent/?exp_lo=5233&exp_hi=&full=1"] this is new[/URL]. I marked in red to be easy to see and inserted some spaces into that line[/QUOTE] If you drill down through from the page you linked to, down to mersenne.ca it says it is fully factored and the remaining [URL="http://www.mersenne.ca/exponent/5233"]~1500 digits are PRP[/URL]. Let's not reopen the PRP debate right now. 
[QUOTE=Gordon;443783]If you drill down through from the page you linked to, down to mersenne.ca it says it is fully factored and the remaining [URL="http://www.mersenne.ca/exponent/5233"]~1500 digits are PRP[/URL].
Let's not reopen the PRP debate right now.[/QUOTE] That was nothing about reopening any debate, and I don't know anything about any "PRP debate". What is there to debate about PRPs? Or you want to say that a ~1500 digits number is difficult to prove prime (or composite), with the hardware and the algorithms we have today? 
[QUOTE=LaurV;443785]That was nothing about reopening any debate, and I don't know anything about any "PRP debate". What is there to debate about PRPs?[/QUOTE]
[STRIKE]I am also mystified. What is being debated about PRP?[/STRIKE] I think the "debate" is about whether a probable prime cofactor means an exponent is truly "fully factored" or not. There was an old thread where people spent dozens of pages arguing vehemently over it. In this case it's a moot point, since this particular prime is easily within range of formal provability using primality certificates issued by primo or similar program. A few weeks ago I started doing ECM on very small exponents with already known factor(s). Currently taking the M5000 range to B1=3,000,000 (i.e., "40 digits"), which means a few thousand curves per exponent. So far I've found new factors for [URL="http://www.mersenne.org/report_exponent/?exp_lo=4957&full=1"]M4957[/URL], [URL="http://www.mersenne.org/report_exponent/?exp_lo=5023&exp_hi=&full=1"]M5023[/URL], and [URL="http://www.mersenne.org/report_exponent/?exp_lo=5233&exp_hi=&full=1"]M5233[/URL] (the latest result). This has been just using Prime95, without GMPECM, but I will soon try that for stage 2. Machines have gotten faster over the years and the time seems ripe to revisit this range in a thorough and systematic way. People have been throwing a lot of effort at the very stubborn M12xx holdouts, but there is some lowhanging fruit in the higher singledigitthousands range. So far I've been using only one core of a machine that's a few years old, but encouraged by this PRP result, I'm going to throw some more cores at it in the cloud. I've also been doing some ECM on alreadyfactored exponents in the 40K and 50K ranges. The most tedious part is creating the "known factors" string at the end of the ECM2= line, but I have a Python script that automates that. 
P1 found a factor in stage #1, B1=665000.
UID: Jwb52z/Clay, M79423907 has a factor: 2357613551541984781291234249 (P1, B1=665000) 90.929 bits. 
Someone (not me) found a big one, the first known factor of [URL="http://www.mersenne.org/report_exponent/?exp_lo=5879&full=1"]M5879[/URL]:
3381116440321017148580653633902983992991015840485797617951 58 digits, 192 bits. 
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