[QUOTE=birtwistlecaleb;588367]Disclaimer: You may not see these in mersenne.ca, but this is probably because I self assigned them.[/QUOTE]Wait 24 hours and they should show up on mersenne.ca It does its data pull overnight in the US o A.
(They are there now.)

[QUOTE=Uncwilly;588368]Wait 24 hours and they should show up on mersenne.ca It does its data pull overnight in the US o A.
(They are there now.)[/QUOTE]
Ah, didn't know. Can you edit my message? (And add that there will be 1,830,XXX,XXX numbers too)

[QUOTE=birtwistlecaleb;588367]You may not see these in mersenne.ca, but this is probably because I self assigned them[/QUOTE]Everything on mersenne.org should show up on mersenne.ca, albeit after a delay of up to 24.5h -- new [i]factors[/i] are pulled in every hour (from [URL="https://www.mersenne.org/report_recent_cleared/"]recent cleared report[/URL]), whereas the detailed work information (who what when how) is pulled in every night about 00:30h UTC.

A related warning: exponent pages on mersenne.ca are heavily cached, if you look at the page after the factor is discovered but before the full nightly sync, subsequent page views may not show the full details, but Ctrl-F5 forcible refresh will fix that.

[url]https://www.mersenne.ca/json2bbcode.php[/url] may be useful to you in formatting results to post in this thread with automatic linking to both mersenne.org and mersenne.ca (and bit size).

Dylan found a nice composite:
[M]M4900289[/M] has a 197.901-bit (60-digit) [b]composite[/b] (P30+P31) factor: [url=https://www.mersenne.ca/M4900289]375214712823873127465912884273993479895231432491081329619849[/url] (P-1,B1=2350000,B2=213850000)

Today, for the first time ever, my machine found a composite factor composed of three factors, of an exponent trial factored to 71 bits:

[URL="https://www.mersenne.ca/exponent/9141029"]https://www.mersenne.ca/exponent/9141029[/URL]

Just before, in the morning it found a 114 bits factor ranking 12th in my personal top 500 and two hours later a regular 92 bits factor.

[QUOTE=tha;588759]a composite factor composed of three factors[/quote]A rare find! :whee:

[M]M9141029[/M] has a 245.684-bit (74-digit) [b]composite[/b] (P23+P24+P28) factor: [url=https://www.mersenne.ca/M9141029]90805179079635333458558529873927662467378423913017841891392559441607383569[/url] (P-1,B1=2000000,B2=146000000)

P-1 found a factor in stage #1, B1=763000.
UID: Jwb52z/Clay, M106358779 has a factor: 282917789511750372931085031635362975391 (P-1, B1=763000),

I think this might be my biggest factor, ever!

127.734 bits!

[QUOTE=Jwb52z;588762]I think this might be my biggest factor, ever! 127.734 bits![/QUOTE]No doubt about it, and by a full 10 bits too!
[url]https://www.mersenne.ca/userfactors/any/789/bits[/url]

[QUOTE=Jwb52z;588762]P-1 found a factor in stage #1, B1=763000.
UID: Jwb52z/Clay, M106358779 has a factor: 282917789511750372931085031635362975391 (P-1, B1=763000),

I think this might be my biggest factor, ever!

127.734 bits![/QUOTE]

mersenne.ca agrees with the statement. Congratulations!

Additionally, it's stage 1 only, so really impressive! (k = 5 × 37 × 251 × 1493 × 2203 × 9533 × 25301 × 59467 × 607147)

M1960050767 has a factor: 2681764646543406705689 [TF:68:72:mfaktc 0.21 barrett76_mul32_gs]

k=2^2*11^2*349*4049977

[QUOTE=Stargate38;588868]M1960050767 has a factor[/QUOTE]
If you mean >1G factors, There are plenty of them. Really easy to find :)
M9936653029 has a factor: 213977058851543423
M9936653539 has a factor: 246744834363283577
M9936654059 has a factor: 272196433996068913
M9936654521 has a factor: 591144276498767839
M9936654757 has a factor: 728248663011034327
M9936654911 has a factor: 1037904750655600609
M9936655019 has a factor: 1007399390014580737
M9936655051 has a factor: 212091622097602769
M9936656221 has a factor: 951250388947975799
M9936656707 has a factor: 433804860337259969
M9936656729 has a factor: 307538631463444391
M9936657383 has a factor: 264243303974865209
M9936657853 has a factor: 888262011431568497
M9936657859 has a factor: 201544436421468281

[QUOTE=Zhangrc;588890]If you mean >1G factors, There are plenty of them. Really easy to find :)[/QUOTE]

It doesn't have to be a particularly noteworthy factor for Stargate to be fond of it. (Re-read the thread title.) Now, if we start adding sub-64-bit factors here, that may be crossing the line.

[M]M3000409[/M] has a 94.882-bit (29-digits) factor: [url=https://www.mersenne.ca/M3000409]36506847546234971967385191137[/url] (P+1, B1=15000000, B2=1530000000)
This is my first factor found using the P+1 method. The previous 36 attempts were unsuccessful.
Success is diminished by the fact that this is the second factor for this Mersenne number :confused:

[QUOTE=Miszka;588962]Success is diminished by the fact that this is the second factor for this Mersenne number :confused:[/QUOTE]

That doesn't diminish the success. What does diminish it is the fact that this is a stealth P-1 factor. i.e. Had you done P-1 to the same bounds, it would have found the factor quicker.

[QUOTE=axn;588964]That doesn't diminish the success. What does diminish it is the fact that this is a stealth P-1 factor. i.e. Had you done P-1 to the same bounds, it would have found the factor quicker.[/QUOTE]
In this case that would indeed be the case, but as I reviewed some results of the P+1 method there are many times when the P-1 method would not produce a result faster. e. g. [M]1891277[/M]
Unfortunately, it is impossible to predict which method will prove more effective in a particular case.

[QUOTE=Miszka;588966]I reviewed some results of the P+1 method there are many times when the P-1 method would not produce a result faster[/QUOTE]You can see from the [url=https://www.mersenne.ca/pplus1.php]list of successful P+1 efforts[/url] that it's a pretty even split between whether the factor could have been found by P-1 or not.

[QUOTE=James Heinrich;588986]You can see from the [url=https://www.mersenne.ca/pplus1.php]list of successful P+1 efforts[/url] that it's a pretty even split between whether the factor could have been found by P-1 or not.[/QUOTE]

Very interesting list!

[M]M6220651[/M] has a 96.568-bit (30-digit) factor: [url=https://www.mersenne.ca/M6220651]117465933684061090230298707631[/url] (P-1,B1=3000000,B2=243000000)


96 bits. at this exponent size, this is a beauty.

Not the normal kind of factor posted here, but I was YAFU'ing a C107 that was already ECM'd appropriately, but YAFU 1.34 likes to recalculate ECM effort and do a few more curves, which actually worked beautifully this time:[code]current ECM pretesting depth: 35.52
scheduled 67 curves at B1=3000000 toward target pretesting depth of 35.67
prp37 = 5217870316310181049264840173981775799 (curve 1 stg2 B1=3000000 sigma=3040696252 thread=0)[/code]The first (second?) curve split the C107=p37+p70
What I expected to take ~8000 seconds took 9.5s :w00t:

Maybe you were looking for [URL="http://mersenneforum.org/showthread.php?t=10029"]this[/URL] thread? :truck:

[SIZE="1"][SPOILER]If I understand correctly, this one is only for factors of Mersenne numbers with prime exponents.[/SPOILER][/SIZE]

[QUOTE=kruoli;590064]Maybe you were looking for [URL="http://mersenneforum.org/showthread.php?t=10029"]this[/URL] thread? :truck:[/QUOTE]I probably was. :redface:

P-1 found a factor in stage #2, B1=756000, B2=20988000.
UID: Jwb52z/Clay, M107023759 has a factor: 15845389801763193699707633 (P-1, B1=756000, B2=20988000)

83.712 bits.

Nothing spectacular, but the first P-1 tests I did in a while and the first to finish stage 1 returned:

[CODE][Worker #3 Oct 24 07:53] P-1 found a factor in stage #1, B1=779000.
[Worker #3 Oct 24 07:53] M107043329 has a factor: 9773787110913045103371451921 (P-1, B1=779000)

k = 45653415314246463240 = 2^3 × 3^3 × 5 × 11 × 21841 × 317797 × 553649[/CODE]

P-1 found a factor in stage #1, B1=756000.
UID: Jwb52z/Clay, M107072687 has a factor: 95352689558688112327801 (P-1, B1=756000)

76.336 bits.

[M]M6234491[/M] has a 107.827-bit (33-digit) factor: [url=https://www.mersenne.ca/M6234491]287831359132009723766012795757047[/url] (P-1,B1=3000000,B2=243000000)


k=23 × 223 × 277 × 129 971 × 627 611 × 199 185 461

[URL="https://www.mersenne.ca/exponent/5551831"]Sometimes you just have to laugh at stats...[/URL]

This was a "one-off" timing test.

[M]M260543[/M] has a 102.431-bit (31-digit) factor: [URL="https://www.mersenne.ca/M260543"]6833981637847127989838565387041[/URL] (ECM,B1=1000000,B2=162000000,Sigma=3342767857012760)
That's the 9th known factor, Seth_Tr found the 8th factor in May.


[M]M194653[/M] has a 124.361-bit (38-digit) factor: [URL="https://www.mersenne.ca/M194653"]27323512924583858950580510798298798737[/URL] (ECM,B1=3000000,B2=477000000,Sigma=6798721071652496)
That's the [B]10th known factor[/B] :smile:, I found the 9th factor 2 months ago.

[QUOTE=nordi;592131][M]M260543[/M] has a 102.431-bit (31-digit) factor: [URL="https://www.mersenne.ca/M260543"]6833981637847127989838565387041[/URL] (ECM,B1=1000000,B2=162000000,Sigma=3342767857012760)
That's the 9th known factor, Seth_Tr found the 8th factor in May.


[M]M194653[/M] has a 124.361-bit (38-digit) factor: [URL="https://www.mersenne.ca/M194653"]27323512924583858950580510798298798737[/URL] (ECM,B1=3000000,B2=477000000,Sigma=6798721071652496)
That's the [B]10th known factor[/B] :smile:, I found the 9th factor 2 months ago.[/QUOTE]

:showoff::tu:

[quote=TheJudger][M]M114860849[/M] has a 224.754-bit (68-digit) [b]composite[/b] (P32+P37) factor: [url=https://www.mersenne.ca/M114860849]45453803780256165659829228890363539404384826272845623290616298112337[/url] (P-1,B1=811000,B2=24076000,E=12)[/quote]Even just one component of that composite factor is #71 on the [url=https://www.mersenne.ca/userfactors/pm1/1/bits]biggest P-1 factors[/url] list.

[M]M2003191[/M] has a 97.506-bit (30-digits) factor: [url=https://www.mersenne.ca/M2003191]225007102354851248019601430113[/url] (P+1, B1=30000000, B2=1620000000)
This is my second factor found using the P+1 method.
This time there is a first factor for this Mersenne number.

P-1 found a factor in stage #2, B1=757000, B2=21023000.
UID: Jwb52z/Clay, M107203427 has a factor: 260429952341275128058663 (P-1, B1=757000, B2=21023000)

77.785 bits.

[QUOTE=TheJudger]
[M]M114860849[/M] has a 224.754-bit (68-digit) composite (P32+P37) factor: 45453803780256165659829228890363539404384826272845623290616298112337 (P-1,B1=811000,B2=24076000,E=12)[/QUOTE]
Congratulations, as that's not a very common accomplishment!
In my "merchandise" I have a factor that is a tad smaller 19147642464835832222111776488276027610060674573088897824886038321359 - 223. 506 bits [M]M3146833[/M]

P-1 found a factor in stage #1, B1=757000.
UID: Jwb52z/Clay, M107207129 has a factor: 98058773655358447592735572577 (P-1, B1=757000)

96.308 bits.

Found my largest P-1 prime factor to date. 128 bits!

[QUOTE][Tue Nov 16 23:14:04 2021]
P-1 found a factor in stage #2, B1=789000, B2=22834000, E=6.
UID: ixfd64/dt-lab-26, M112991353 has a factor: 228447809578680398866569621097916626871 (P-1, B1=789000, B2=22834000, E=6), AID: 89CC27EABD59FDBCBDF20BC67B203E7F[/QUOTE]

:toot:

[QUOTE=ixfd64;593344]Found my largest P-1 prime factor to date. 128 bits![/QUOTE]

Nice. But... E=6?! What version of P95 are you using?

[QUOTE=axn;593352]Nice. But... E=6?! What version of P95 are you using?[/QUOTE]v30.3.6

Time to upgrade?

P-1 found a factor in stage #2, B1=759000, B2=21076000.
UID: Jwb52z/Clay, M107472557 has a factor: 2175775820816119586199479 (P-1, B1=759000, B2=21076000)

80.848 bits.

My first P-1 factor:

UID: slandrum/BB2, M115047523 has a factor: 26766179697464143575646837913 (P-1, B1=846000, B2=25442000, E=6)

94.4 bits

:groupwave:

M[M]107476399[/M] has a factor: 15352799235581412298952661367

Nothing impressive for P-1 (94 bits) but my last F-PM1 was almost 100 tests ago. I was starting to think I had a hardware problem.

[QUOTE=techn1ciaN;593769]M[M]107476399[/M] has a factor: 15352799235581412298952661367

Nothing impressive for P-1 (94 bits) but my last F-PM1 was almost 100 tests ago. I was starting to think I had a hardware problem.[/QUOTE]

Been there.
Over 56,000 attempts I average a factor every 30 or 40 but have seen stretches as high as 373 with no factor....and every time I have a bad stretch I still want to suspect the hardware....then they snap out of it and make up for lost time.

Patience is a virtue. :whistle:

Two factors found while DC PM1'ing exponents with poor (stage 1 only) PM1 :smile:

[M]59794643[/M] with factor 758607030356942234110073 (79.328 bits)


[M]60167521[/M] with factor 108612809058959125048583449 (86.489 bits)

[QUOTE=axn;593383]Time to upgrade?[/QUOTE]

I probably will when the stable version is available!

My first P+1 factor and even a relatively large one and a relatively smooth one and of a relatively small Mersenne number:

[CODE][URL="https://www.mersenne.ca/exponent/211231"]M211231[/URL]
Start=2/7, B1=150,000,000, Factor: 44020293565604983870643000656007 (32 digits, 105.1 bits)
P+1 = 2^3 * 3 * 17^2 * 83 * 157 * 2441 * 258337 * 17578577 * 43936757[/CODE]

M[M]997577587[/M] has a factor: 11562860692189321253647

M[M]997571873[/M] has a factor: 18373625784649599011423

M[M]997570663[/M] has a factor: 14100309041276501026441

M[M]997564333[/M] has a factor: 13823818175199038095129

M[M]997561469[/M] has a factor: 17272242508747031148527

M[M]997557647[/M] has a factor: 18246811250485963666177

M[M]997557367[/M] has a factor: 13755089029976709478417

M[M]997555331[/M] has a factor: 13188178428948819158353

I usually TF at the DC wavefront, but I've been having a dry streak of more than 300 exponents there. I loaded about 600 of these 997,xxx,xxx exponents as a hardware sanity check since they run so quickly at current TF levels. Conclusion: lack of DC luck is indeed just that, bad luck.

Interestingly, my throughput in GHz-days / day is substantially better with DC-range exponents (60–65 M) than with these huge 997 M ones — appx. 970 versus appx. 850. I optimized my MFaktC config by trial and error with a DC-range test exponent, so I thought this might be an artifact of that, but I tried various tweaks and none produced an improvement.

Another one, 37 digits, the largest one found by P+1 so far, though admittedly it was found at the P-1 part (it's not P+1 smooth at all).

[CODE][URL="https://www.mersenne.ca/exponent/214069"]M214069[/URL]
Start=2 / 7, B1=150000000, B2=12750000000, Factor: 1765947009958424280438725602396032049 (37 digits, 120.4 bits)
P+1 = 2 * 5^2 * 101 * 31723 * 2573471 * 4283440708731964743577
k = 2^3 × 3^2 × 7^2 × 29 × 31 × 757 × 68687 × 3287507 × 7607965061[/CODE]

Feels like I've saved a lamb from the slaughter on this one:
[M]107415289[/M] (factor=67834286362972615909729897, 85.871 bits), it was expired as a PRP test and assigned (very close to cat 0, but still cat 1) to me as P-1, I prioritized it and ran it with tests_saved=1 as to make it less likely to hold up a milestone down the line!


Also, TF came up with a factor today:
[M]108617059[/M] (factor=144166210879913180106767, 76.932 bits)

P-1 found a factor in stage #2, B1=794000, B2=21764000.
UID: Jwb52z/Clay, M108035089 has a factor: 130233006903988384213171714266285847938196943239024729226893649081 (P-1, B1=794000, B2=21764000)
I know it's a composite factor. Unbroken it's a whopping 216.306 bits. It can be broken down into these two factors: 6384544128130228761451969, which is 82.401 bits and 20398168497290705231363540518336781235449, which is 133.906 bits.

M[M]332999839[/M] has a factor: 147083513208787881114937

I've been looking at the beginning of the 100M-digit range in the database recently and most 100M-digit primality tests seem to go out with non-optimal TF (in some cases, the primality tester even has to do the last few bit levels of the PrimeNet TF release threshold). I'm getting "lowest bit levels" TF assignments for the range 332.2 M – 333 M and trying to bring the worst examples up a bit. If I get lucky enough I might even "DC" an exponent with an existing single C-LL or unproofed C-PRP result.

[QUOTE=Jwb52z;594962]P-1 found a factor in stage #2, B1=794000, B2=21764000.
UID: Jwb52z/Clay, M108035089 has a factor: 130233006903988384213171714266285847938196943239024729226893649081 (P-1, B1=794000, B2=21764000)
I know it's a composite factor. Unbroken it's a whopping 216.306 bits. It can be broken down into these two factors: 6384544128130228761451969, which is 82.401 bits and 20398168497290705231363540518336781235449, which is 133.906 bits.[/QUOTE]

You can be proud of this result :victor:

[QUOTE=Jwb52z;594962][M]M108035089[/M] has a 216.306-bit (66-digit) [b]composite[/b] (P25+P41) factor: [url=https://www.mersenne.ca/M108035089]130233006903988384213171714266285847938196943239024729226893649081[/url] (P-1,B1=794000,B2=21764000)
I know it's a composite factor. Unbroken it's a whopping 216.306 bits. It can be broken down into these two factors: 6384544128130228761451969, which is 82.401 bits and 20398168497290705231363540518336781235449, which is 133.906 bits.[/QUOTE]The larger of the two ranks #82 in the [url=https://www.mersenne.ca/userfactors/pm1/1/bits]biggest P-1 factors list[/url], impressive in its own right, plus another 82-bit factor on the side. :cool:

How often does that list update? I clicked it and number 82 is not my factor now.

[QUOTE=Jwb52z;594999]How often does that list update? I clicked it and number 82 is not my factor now.[/QUOTE]mersenne.ca gets the day's activity from mersenne.org just after midnight UTC, so factoring in processing time you can probably expect to see your factor on the list sometime around 01:00h UTC the day after discovery.
Note that factors themselves are spidered hourly, but the who-when-how of factoring effort is not known until the day is complete.

P-1 found a factor in stage #1, B1=763000.
UID: Jwb52z/Clay, M108066799 has a factor: 185428332419676038195353 (P-1, B1=763000)

77.295 bits.

my biggest so far
[M]M8538269[/M] has a 129.728-bit (40-digit) factor: [URL="https://www.mersenne.ca/M8538269"]1127043861162808113814773315610463390639[/URL] (P-1,B1=1000000,B2=330325710)


and a top record, it seems

When it rains, it pours: I am going through unverified 60.50M-60.55M exponents which only had stage 1 P-1 done and for one week (30 or so exponents) no factors were found. Now I noticed finally a factor was found:

[CODE][URL="https://www.mersenne.ca/exponent/60545327"]M60545327[/URL]
Factor: 47949826513996019108681 / (P-1, B1=2000000, B2=174051780)
23 digits, 75.34 bits
k = 2^2 × 5 × 19 × 53 × 1361 × 14446373[/CODE]

And just while looking at it another result came in and yet another factor!

[CODE][URL="https://www.mersenne.ca/exponent/60545941"]M60545941[/URL]
Factor: 1373855333786231688655366993 / (P-1, B1=2000000)
28 digits, 90.15 bits
k = 2^3 x 3 x 7 x 89 x 24517 x 41389 x 747781[/CODE]

Now I only need a factor from my GPU72 colab and I'm happy ...

This one was found by ramgeis, not by me, but I'm still fond of it:


[URL="https://www.mersenne.ca/exponent/3356318939"]M3356318939[/URL] has a 84.652-bit (26-digit) factor: 30392108107422786794726689


This makes M3,356,318,939 only the fourth Mersenne number with [URL="https://www.mersenne.ca/manyfactors.php"]11 known prime factors.[/URL]

I'm also fond of that factor! I found the 10th factor for that number as part of my manyfactor push in Aug/Sep!

[QUOTE=bur;595367]Now I only need a factor from my GPU72 colab and I'm happy ...[/QUOTE]When it pours, it pours:

[CODE][URL="https://www.mersenne.ca/exponent/26243381"]M26243381[/URL]
Factor: 112490608941576463743381329 / (P-1, B1=933000, B2=48804000) (27 digits, 86.5 bits)
k = 2^3 × 61 × 18541 × 31267 × 7575779

[URL="https://www.mersenne.ca/exponent/26243527"]M26243527[/URL]
Factor: 46280261033081507464609 / (P-1, B1=933000) (23 digits, 75.3 bits)
k = 2^4 × 3 × 23 × 41 × 32119 × 606497[/CODE]

Not to get greedy, but now a TF factor from colab would be nice.


And another from the "factoring unverified exponents":

[CODE][URL="https://www.mersenne.ca/exponent/60546041"]M60546041[/URL]
Factor: 46280261033081507464609 / (P-1, B1=933000) (35 digits, 113.9 bits)
k = 11 × 269 × 337 × 397 × 1321 × 7549 × 20879 × 2001371[/CODE]


I'm beginning to wonder if my B1=2M bound for the 60.5M exponents is too large since all three factors could have been found with B1=500K, B2=50M or similar. I chose that relatively large B1 because I didn't want someone else to have to go over the same range again in 5 years with incrased B1.

[QUOTE=bur;595463].... I chose that relatively large B1 because I didn't want someone else to have to go over the same range again in 5 years with incrased B1.[/QUOTE]

This has been my logic, too. The existence of smaller factors / factors that could have been found with smaller bounds shouldn't change your attitude, imo. Do it once, do it right!

[QUOTE=petrw1;593778]Been there.
Over 56,000 attempts I average a factor every 30 or 40 but have seen stretches as high as 373 with no factor....and every time I have a bad stretch I still want to suspect the hardware....then they snap out of it and make up for lost time.

Patience is a virtue. :whistle:[/QUOTE]Poisson could have told you that ...

One man's fish is another man's poisson.

[QUOTE=VBCurtis;595498]This has been my logic, too. The existence of smaller factors / factors that could have been found with smaller bounds shouldn't change your attitude, imo. Do it once, do it right![/QUOTE]Yea, you're right, I just prepared a worktodo.add with just pfactor for a faster turnover, but I'll revert it to B1=2M... ;)

[QUOTE=xilman;595506]One man's fish is another man's poisson.[/QUOTE]
Also, one man's [I]gift [/I]is another man's poison.

ECM found a factor in curve #3, stage #2. Sigma=6233557776964751, B1=250000, B2=23250000.

M697397 has a factor: 9063851744869270329116505270383 (ECM curve 3, B1=250000, B2=23250000)

It has been quite a while since I found one of these. I cannot use the bit calculator on [I]mersenne.ca[/I]. It keeps disappearing when I hover over the box. Oh well.

[QUOTE=storm5510;595788]ECM found a factor in curve #3, stage #2. Sigma=6233557776964751, B1=250000, B2=23250000.

M697397 has a factor: 9063851744869270329116505270383 (ECM curve 3, B1=250000, B2=23250000)

It has been quite a while since I found one of these. I cannot use the bit calculator on [I]mersenne.ca[/I]. It keeps disappearing when I hover over the box. Oh well.[/QUOTE]
Number of bits in the positive integer N is

1 + floor(log(N)/log(2))

In Pari-GP, you can also use

#binary(N)

[code]? #binary(9063851744869270329116505270383)
%1 = 103[/code]

Nice find!

[b]EDIT:[/b] An alternate interpretation of "bits" is simply log(N)/log(2).[code]? log(9063851744869270329116505270383)/log(2)
%1 = 102.83796711017436436382918177786544610[/code]

[QUOTE=storm5510;595788]I cannot use the bit calculator on [I]mersenne.ca[/I]. It keeps disappearing when I hover over the box.[/QUOTE]It seems to be working as expected for me. If it sits inconveniently on your screen you can also use the version at [URL="https://www.mersenne.ca/sitemap"]mersenne.ca/sitemap[/URL]
Or use the [URL="https://www.mersenne.ca/json2bbcode.php"]BBcode converter[/URL] to give you pretty output like:[quote][M]M697397[/M] has a 102.838-bit (31-digit) factor: [url=https://www.mersenne.ca/M697397]9063851744869270329116505270383[/url] (ECM,B1=250000,B2=23250000)[/quote]

[QUOTE=James Heinrich;595809]It seems to be working as expected for me. If it sits inconveniently on your screen you can also use the version at [URL="https://www.mersenne.ca/sitemap"]mersenne.ca/sitemap[/URL]
Or use the [URL="https://www.mersenne.ca/json2bbcode.php"]BBcode converter[/URL] to give you pretty output like:[/QUOTE]

It many have different behaviors based on the web browser used. Sometimes, I use Edge and other times Firefox. I know, it does not make any sense to use two. In any case, I believe my previous record was 29 digits, also ECM. I had it in a text file, but cannot find it now. I may have stored it away somewhere.

Many thanks! :smile:

[QUOTE=storm5510;595971]I believe my previous record was 29 digits, also ECM. I had it in a text file, but cannot find it now. I may have stored it away somewhere.[/QUOTE]Your [URL="https://www.mersenne.ca/userfactors/ecm/63934/bits"]previous record[/URL] was in fact [b]3[/b]9 digits.

[QUOTE=James Heinrich;595973]Your [URL="https://www.mersenne.ca/userfactors/ecm/63934/bits"]previous record[/URL] was in fact [b]3[/b]9 digits.[/QUOTE]

Oh! My bad. :blush:

M[M]109101319[/M] has a factor: 89994947583983983892401

First find for my old laptop that I just dug out and set to doing P-1. It's fairly low-end (two-core Zen+, 8 GB RAM) and can finish maybe two wavefront P-1 runs a day with [c]tests_saved=1[/c], so hitting pay dirt within two exponents was a pleasant surprise (and a handy confirmation of hardware functionality).

Interestingly, this factor could also have been found with TF77.

Using the P-1method and version mprime 30.8 on a 64 GB machine I found a factor for M9509161.

The factor itself is a rather normal one: 493379850346175773054490527.

The fun is in the factoring of k, it yields: 32 × 11 × 47 × 109 × 16921 × 3022898999.

The 3022898999 is very narrow under the B2 limit of 3089082150.

[QUOTE=techn1ciaN;596184]M[M]109101319[/M] has a factor: 89994947583983983892401

First find for my old laptop that I just dug out and set to doing P-1. It's fairly low-end (two-core Zen+, 8 GB RAM) and can finish maybe two wavefront P-1 runs a day with [c]tests_saved=1[/c], so hitting pay dirt within two exponents was a pleasant surprise (and a handy confirmation of hardware functionality).

Interestingly, this factor could also have been found with TF77.[/QUOTE]

This is a rather smooth factor and should be found in stage 1.
Is stage 1 GCD deprecated?

No, but you can skip the stage1 GCD

Hopefully I am not saying something that I should not...

masser found a mass(er)ive one!
[M]M8639051[/M] has a 148.409-bit (45-digit) factor: [url=https://www.mersenne.ca/M8639051]473925524306620205153987295206898877469479169[/url] placed 15th in the top P-1 list!

[QUOTE=kruoli;596836]Hopefully I am not saying something that I should not...

masser found a mass(er)ive one!
[M]M8639051[/M] has a 148.409-bit (45-digit) factor: [url=https://www.mersenne.ca/M8639051]473925524306620205153987295206898877469479169[/url] placed 15th in the top P-1 list![/QUOTE]

I was curious how long it would take someone to notice that one. It's a beast!

[M]M12086257[/M] has a 232.056-bit (70-digit) [B]composite[/B] (P21+P22+P28) factor: [URL="https://www.mersenne.ca/M12086257"]7175325903126100642770883886258989157868691603487785881027652989293479[/URL] (P-1,B1=400000,B2=275121000)


My very first triple factor. :cool:

[QUOTE=nordi;597092]My very first triple factor. :cool:[/QUOTE]Ooh, pretty! :cool:

[M]108316331[/M]

4748876008595777234809387978603489

B1=1070000, B2=204164730

111.871 bits

[QUOTE=Batalov;595540]Also, one man's gift is another man's poison.[/QUOTE]Das ist korrekt.


In other news, I got excited about a 51 digit P-1 factor. Turned out it were two factors, but that's still nice, especially since it came from free Colab via GPU72:

[CODE][URL=https://www.mersenne.ca/exponent/21747997]M21747997[/URL]
(P-1, B1=799000, B2=42406000)

Factor: 111450262682214711089353
k = 2^2 × 3^2 × 7^2 × 613673 × 2366989

Factor: 2198130602062734345911531551
3 × 5^2 × 7^2 × 11 × 53 × 71 × 170749 × 1945637[/CODE]

[M]M8579873[/M] has a 123.322-bit (38-digit) factor: [url=https://www.mersenne.ca/M8579873]13293461509110533295456570028915625897[/url] (P-1,B1=1560000,B2=627605550)

[m]M13215599[/m] has a composite factor: 156983032676499216249507946592486467212604643431265282431 (186.679 bits) = 32454152674998424032372319 (84.747 bits) * 4837070751732600558995351425249 (101.932 bits).

George just found a pretty one ([url=https://www.mersenne.ca/userfactors/pm1/1/bits]#16 biggest ever[/url]):[quote][M]M80309[/M] has a 148.041-bit (45-digit) factor: [url=https://www.mersenne.ca/M80309]367135192227544403816033004684216729776734999[/url] (P-1,B1=1000000000,B2=20461169718990)[/quote]

[QUOTE=James Heinrich;597658]George just found a pretty one ([url=https://www.mersenne.ca/userfactors/pm1/1/bits]#16 biggest ever[/url]):[/QUOTE]I noticed that the (last 16 hex digits of the) C-PRP residues listed for

M80309/10572519233/367135192227544403816033004684216729776734999 and

M80309/10572519233

were the same. Is there some obvious reason for this?

(My wits are presently addled by symptoms of a head cold...)

[QUOTE=Dr Sardonicus;597678]I noticed that the (last 16 hex digits of the) C-PRP residues listed for
M80309/10572519233/367135192227544403816033004684216729776734999 and
M80309/10572519233
were the same. Is there some obvious reason for this?[/QUOTE]This is normal and expected. PRP residues are always the same, no matter how many known factors are included (assuming same PRP-type). I don't pretend to understand [i]why[/i], I just know that it is. Note that the "type" (e.g. 1, 5) of the PRP will lead to different residues, but the number of known factors (also "shift" value) do not affect the residue. Here's another small exponent with a recent factor that shows both conditions: [m]M80471[/m] -- three PRP-type-1 on 4 factors, of which one is shifted, then a prp-type-5 on same 4 factors, now another prp-type-5 on 5 factors.

[QUOTE=James Heinrich;597686]This is normal and expected. PRP residues are always the same, no matter how many known factors are included (assuming same PRP-type).
<snip>[/QUOTE]I found an [url=https://mersenneforum.org/showthread.php?t=26448]earlier thread[/url] bringing up this [strike]bug[/strike] feature.

The OP in that thread seems to say that when subsequent PRP-CF tests say C, the new PRP-CF residue [i]replaces[/i] previous PRP-CF residues. This would certainly account for all reported PRP-CF residues being the same (assuming the remaining cofactor has tested composite).

Why this would be done is beyond me, but the only alternative explanation that fits the facts seems to be that, as long as the remaining CF has tested composite, the original PRP residue is simply repeated. There may be good reasons for not publishing the sequence of actual PRP residues (mod 16[sup]16[/sup]) for the composite cofactors, of which I am ignorant. [I am rejecting the idea that the residues (mod 16[sup]16[/sup]) from the PRP-CF tests are all actually the same.]

Of course, if the remaining CF tests as a PRP, the "all PRP residues are the same" goes out the window, and the residue is reported as PRP_PRP_PRP_PRP_ .

As I mentioned in that other thread, the residues produced are the same. You're assuming PRP-CF does a standard Fermat test; it does NOT.

Let N=Mp/f
Instead of checking 3^(N-1)==1 (mod N) (equivalently 3^N==3 (mod N)), it computes 3^(N*f+1)=3^(Mp+1)==3^(f+1) (mod N)

Note. 3^N==3 ==> 3^Nf == 3^f ==> 3^(Nf+1) == 3^(f+1)

This gives rise to same residue, since we're always computing the same expression 3^(Mp+1).

Advantages:
1) Each run produces same residue, hence multiple runs acts as additional checks on previous runs.
2) Since the modified computation is just a series of squarings, it is now amenable to GEC and CERT.

[QUOTE=axn;597761]<snip>
Let N=Mp/f
Instead of checking 3^(N-1)==1 (mod N) (equivalently 3^N==3 (mod N)), it computes 3^(N*f+1)=3^(Mp+1)==3^(f+1) (mod N)
<snip>[/QUOTE]As I understand it, a PRP test on M = M[sub]p[/sub] checks 3^(M + 1) to see whether it's 9 (mod M).

I had actually thought of the possibility that subsequent tests were simply looking at 3^(M + 1) (mod N) where N is the cofactor; N divides M = M[sub]p[/sub].

Suppose 3^(M+1) = M*q + R where 0 < R < M. Then, yes, N certainly divides 3^(M+1) - R = M*q = N*f*Q, so R may be considered to be "the residue" in that sense.

However, what I usually think of as the "residue of 3^(M+1) (mod N)" is r, where

3^(M+1) = N*Q + r, and 0 < r < N.

Clearly r is just R reduced mod N. Generally, r will be less than R.

It was not clear to me why R - r would be divisible by 2[sup]64[/sup].

[QUOTE=Dr Sardonicus;597788]As I understand it, a PRP test on M = M[sub]p[/sub] checks 3^(M + 1) to see whether it's 9 (mod M).

I had actually thought of the possibility that subsequent tests were simply looking at 3^(M + 1) (mod N) where N is the cofactor; N divides M = M[sub]p[/sub].

Suppose 3^(M+1) = M*q + R where 0 < R < M. Then, yes, N certainly divides 3^(M+1) - R = M*q = N*f*Q, so R may be considered to be "the residue" in that sense.

However, what I usually think of as the "residue of 3^(M+1) (mod N)" is r, where

3^(M+1) = N*Q + r, and 0 < r < N.

Clearly r is just R reduced mod N. Generally, r will be less than R.

It was not clear to me why R - r would be divisible by 2[sup]64[/sup].[/QUOTE]

But my guess is R is probably what's reported and not r (r is R mod N).

ETA: This means that if the full residue of the PRP were saved, any time a (new) factor were found, the remaining cofactor could be checked against the original residue to see if it's PRP.

[QUOTE=axn;597761]As I mentioned in that other thread, the residues produced are the same. You're assuming PRP-CF does a standard Fermat test; it does NOT.

Let N=Mp/f
Instead of checking 3^(N-1)==1 (mod N) (equivalently 3^N==3 (mod N)), it computes 3^(N*f+1)=3^(Mp+1)==3^(f+1) (mod N)
<snip>
[/QUOTE]OK, looks pretty good. Let's see if I have this straight: M = M[sub]p[/sub] = f*N. We have 3^(M+1) = M*q + R, q integer, 0 < R < M

Now 3^(M+1) = 3^(f*N + 1) = 3^(f*(N-1) + f + 1) = (3^(N-1))[sup]f[/sup] * 3^(f+1). So if 3^(N-1) == 1 (mod N) we have (3^(N-1))[sup]f[/sup] == 1 (mod N), and R == 3^(f+1) (mod N).

Thus, if R =/= 3^(f+1) (mod N), the cofactor N is definitely composite. Done. No standard Fermat test needed.

However, if R == 3^(f+1) (mod N) it does [i]not[/i] follow that N is a base-3 Fermat PRP, i.e. that 3^(N-1) == 1 (mod N). Only that (3^(N-1)))[sup]f[/sup] == 1 (mod N).

I know, gcd(f, eulerphi(N)) would have to be greater than 1 in order for 3^(N-1) [i]not[/i] to be congruent to 1 (mod N).

That seems extremely unlikely to me, and I am confident that no examples are known, but I don't know that it's impossible.

P-1 found a factor in stage #2, B1=766000, B2=25093000.
UID: Jwb52z/Clay, M108524239 has a factor: 952615068857130427852757781191 (P-1, B1=766000, B2=25093000)

99.588 bits.

[M]M8590991[/M] has a 121.408-bit (37-digit) factor: [url=https://www.mersenne.ca/M8590991]3527086255292055773928440628536263153[/url] (P-1,B1=1560000,B2=627605550)
another big one.

Two nice first-factor finds by anonymous:[quote][M]M78301[/M] has a 137.650-bit (42-digit) factor: [url=https://www.mersenne.ca/M78301]273323880097381566755770440603005212056217[/url] (ECM,B1=3000000,B2=300000000,Sigma=1195368452843377)

[M]M65257[/M] has a 135.337-bit (41-digit) factor: [url=https://www.mersenne.ca/M65257]55022097929766288879909228921832648158913[/url] (ECM,B1=3000000,B2=300000000,Sigma=4361375916221119)[/quote]

[M]10404679[/M]: 118793848017180226139209650887 (30 digits, 96.584 bits)

This looks like any old factor... until you take a look at the effort required for this one. Normal P-1 is at 1,069.7 GHz-days and the min. bounds are B1=597,137 and B2=22,193,557,699

Bless version 30.8

[CA]10713539[/CA]

[C]M10713539 has a factor: 9646618965808297396650789217449140593554849484807561 (P-1, B1=3000000, B2=21676825170)

7259945416488565152965177 × 1328745384765454647667709393[/C]

:mike: