It was suggested that ECM often makes more sense on those smaller Mersenne than P-1, and yes, there are a lot of low-hanging fruits with t35 done only partially. 1500 B1=1M curves on a 10 core take about 1.5 days and you can be fairly certain you won't miss any factor < 35 digits with that.

[CODE]First hit:

[URL="https://www.mersenne.ca/exponent/177949"]M177949[/URL]
Factor: 33673305014952064901960880605783657 (35 digits)

ECM B1=1000000, B2=167000000, Sigma=3976350787451175
k = 2^2 × 7 × 113 × 29903617016456689669335223 (boom, take that, P-1)

Group order:
2^4 × 3 × 251 × 3319 × 26111 × 111767 × 477073 × 741043 × 816203
[/CODE]

Don't take this too serious, I did a lot of P-1 and even P+1 and I definitely get the lottery appeal of it with the chance to score big... :)

3 in a row via P1.
 

[CODE]Magic_8_Ball 20824319 NF-PM1 2022-01-21 14:35 0.0 B1=800000, B2=288897180 19.4015
Magic_8_Ball 20824147 F-PM1 2022-01-21 14:17 0.0 Factor: 495235256819022693269729 / (P-1, B1=800000, B2=288897180) 19.4015
Magic_8_Ball 20823619 F-PM1 2022-01-21 13:58 0.0 Factor: 25548786609611112273299959 / (P-1, B1=800000, B2=288897180) 19.4015
Magic_8_Ball 20820379 F-PM1 2022-01-21 13:40 0.0 Factor: 1046110442462024597648707729 / (P-1, B1=800000, B2=288897180) 19.4015
Magic_8_Ball 20818361 NF-PM1 2022-01-21 13:21 0.0 B1=800000, B2=288897180 19.4015[/CODE]

[M]M8180143[/M] has a 210.388-bit (64-digit) [B]composite[/B] (P25+P39) factor: [URL="https://www.mersenne.ca/M8180143"]2153365510583437050044092603818787130235731554764189688651981753[/URL] (P-1,B1=1500000,B2=800578350)

Yeah, my first double factor in one P-1 attempt. And it includes the largest factor, I found so far (#172 in the Top P-1 factor list).

ECM found a factor
 

[M]104297[/M] B1=3000000, B2=447000000, curve 244

33730663290433956450015516054234200283383287

144.597 bits

[M]M14691419[/M] has a 148.225-bit (45-digit) [b]composite[/b] (P23+P23) factor: [url=https://www.mersenne.ca/M14691419]416943345784701035645026212406037518765877617[/url] (P-1,B1=2100000,B2=534604980)


both are 74 bits

[CODE][URL="https://www.mersenne.ca/exponent/21013"]M21013[/URL]
Factor: 262993879056590526599462437387619513220841 (42 digits, 137.6 bits)
B1=3000000, B2=528000000, Sigma=6108330422011107

Group order = 2^2 x 3^5 x 11 x 263 x 643 x 19157 x 20071 x 63331 x 147881 x 652601 x 61893779

k = 2^2 x 3 x 5 x 59 x 242399 x 7292786486304502390480104379[/CODE]
It's the third factor of M21013 (1.56%), remaining co-factor is composite. That factor could have quite likely been found with B1=1M already.

Simon Josefsson has found a factor (7th biggest!)
[M]M108366469[/m] has a factor: 21806524243495451887372970600275462563390077239
(153.933 bits)
Congratulations! :bow wave:

Maybe this means I should buy some lottery tickets???
 

You have to love statistics... :smile:

[CODE]
gpu72ng 11757341 F-PM1 2022-02-03 00:05 6.4 Factor: 18209030934069669978769 / (P-1, B1=2000000, B2=496384980) 18.6152
gpu72 11765911 F-PM1 2022-02-02 23:09 4.3 Factor: 813514493428352514799942217 / (P-1, B1=2000000, B2=496384980) 18.6152
gpu72ng 11757293 F-PM1 2022-02-02 23:03 6.3 Factor: 287095610823108514130103097 / (P-1, B1=2000000, B2=496384980) 18.6152
[/CODE]

[M]M22621[/M] has a third factor:

[CODE][URL="https://www.mersenne.ca/factor/140986430775391680242875594970278954759"]140986430775391680242875594970278954759[/URL] (39 digits, 126.7 bits)
ECM, B1=3M, B2=321M, Sigma=3634941837045978
k = 3^3 × 71 × 31481 × 317371 × 5654288209 × 28775289833[/CODE]

I had trouble with the group order though, it had 17 and 18 digits factors which doesn't agree with the B1/B2 bounds. Switching to parameter=1 didn't help. Does anyone know what I did wrong?

M[M]168628223[/M] has a factor between 2^110 to 2^111: 1469669652995445433018230941584663

[M]M14657387[/M] has a 183.587-bit (56-digit) [b]composite[/b] (P24+P32) factor: [url=https://www.mersenne.ca/M14657387]18413636509265873444254512179821235243842945866131842033[/url] (P-1,B1=2100000,B2=534604980)

Don't you just hate it when something like [URL="https://www.mersenne.ca/exponent/11786351"]this happens...[/URL]

M[M]332250001[/M] has a 79-bit factor: 408432593734312309699081

My third TF success in the low 100M-digit range, and my first at this bit level

M[M]109527281[/M] has a 106-bit P-1 factor: 41531772420988543046370478147111

My first P-1 score > 100 bits.

[M]M14630887[/M] has a 77.155-bit (24-digit) factor: [URL="https://www.mersenne.ca/M14630887"]168255486935289360263863[/URL] (P-1,B1=2100000,B2=534604980)


what is so interesting about it? K is very unsmooth
k=3^4 × 43^2 × 83 × 462 560 519

[QUOTE=firejuggler;599928]<snip>
K is very unsmooth
k=3^4 × 43^2 × 83 × 462 560 519[/QUOTE]Interesting. I have a sneaking hunch that the software might be written to make provision for k having almost all small prime factors, except for a single prime factor larger than the exponent.

Ok ok... but for me it is rare that the difference is so large

[M]M14602481[/M] has a 122.486-bit (37-digit) factor: [url=https://www.mersenne.ca/M14602481]7445406722651794964602916059035754921[/url] (P-1,B1=2100000,B2=534604980)


122 bits! it is a top five!

[QUOTE=firejuggler;600107]Ok ok... but for me it is rare that the difference is so large

[M]M14602481[/M] has a 122.486-bit (37-digit) factor: [url=https://www.mersenne.ca/M14602481]7445406722651794964602916059035754921[/url] (P-1,B1=2100000,B2=534604980)


122 bits! it is a top five![/QUOTE]:party:[code]? q=7445406722651794964602916059035754921;print(factor(q-1))
[2, 3; 3, 1; 5, 1; 23, 1; 661, 1; 743, 1; 825107, 1; 1506943, 1; 14602481, 1; 302520859, 1]
?[/code]

[M]M10674101[/M] has a 128.559-bit (39-digit) factor: [URL="https://www.mersenne.ca/M10674101"]501429461099632378102024867763831999287[/URL] (P-1,B1=1000000,B2=683234370)

:mike:

[QUOTE=Xyzzy;600188][M]M10674101[/M] has a 128.559-bit (39-digit) factor (P-1,B1=1000000,B2=683234370)[/QUOTE]B1 used: 1,000,000 but you could've found it in stage-1 with B1 = 1,058,921 :rogue:

[QUOTE=James Heinrich;600190]B1 used: 1,000,000 but you could've found it in stage-1 with B1 = 1,058,921 :rogue:[/QUOTE]

Killjoy. :davieddy:

[QUOTE=James Heinrich;600190][QUOTE=Xyzzy;600188][M]M10674101[/M] has a 128.559-bit (39-digit) factor (P-1,B1=1000000,B2=683234370)[/QUOTE]B1 used: 1,000,000 but you could've found it in stage-1 with B1 = 1,058,921 :rogue:[/QUOTE]Hmm, why is that? Oh, wait...[code]? q=501429461099632378102024867763831999287;print(factor(q-1))
[2, 1; 3, 3; 13, 1; 109, 1; 139, 1; 397, 1; 1579, 1; 2593, 1; 8273, 1; 310169, 1; [color=red]1058921[/color], 1; 10674101, 1][/code]If only he'd known about that factor of q - 1 before he knew that q was a factor...

[QUOTE=Dr Sardonicus;600195]If only he'd known about that factor of q - 1 before he knew that q was a factor...[/QUOTE]He should've consulted the secret table I keep that lists the k values of all undiscovered factors.

[QUOTE=James Heinrich;600197]He should've consulted the secret table I keep that lists the k values of all undiscovered factors.[/QUOTE]Did Curtis sell that to you?

[QUOTE=James Heinrich;600197]He should've consulted the secret table I keep that lists the k values of all undiscovered factors.[/QUOTE]I would imagine that, for every positive integer k which is not congruent to 2 (mod 4), there are infinitely many primes p for which q = 2*k*p + 1 divides 2^p - 1.

Values of k congruent to 2 (mod 4) are ruled out because q would be congruent to 5 (mod 8), and therefore not a divisor of 2^p - 1.

[QUOTE=Dr Sardonicus;600219]I would imagine that, for every positive integer k which is not congruent to 2 (mod 4), there are infinitely many primes p for which q = 2*k*p + 1 divides 2^p - 1.

Values of k congruent to 2 (mod 4) are ruled out because q would be congruent to 5 (mod 8), and therefore not a divisor of 2^p - 1.[/QUOTE]

I guess it's not secret anymore :lol::razz:

[QUOTE=Viliam Furik;600231]I guess it's not secret anymore :lol::razz:[/QUOTE]

Is this anything to do with Legendre's theorem: All primitive prime factors of a (homogeneous) Cunningham number have the form [I]kn[/I] + 1. If n is odd they have the form 2[I]kn[/I] + 1. Alternatively: all primitive prime factors are congruent to 1 modulo [I]n[/I] if [I]n[/I] is even and 2[I]n[/I] if [I]n[/I] is odd.

M14 653 103 has 76.7 bit factor :122734318525096261632697
[url]https://www.mersenne.ca/exponent/14653103[/url]

This was missed by an earlier P-1

[M]M10694611[/M] has a 131.385-bit (40-digit) factor: [URL="https://www.mersenne.ca/M10694611"]3554057355364082639398093556551855458167[/URL] (P-1,B1=1000000,B2=683234370)

:mike:

[M]M13799479[/M] has a 197.019-bit (60-digit) [b]composite[/b] (P28+P33) factor: [url=https://www.mersenne.ca/M13799479]203567302892764010174130301907774551633686861729505640138639[/url] (P-1,B1=531000,B2=492104340)

M[M]65330107[/M] has a 74.99-bit factor: 37530453286101721709273

For every instance of this:[QUOTE=chalsall;599558]Don't you just hate it when something like [URL="https://www.mersenne.ca/exponent/11786351"]this happens...[/URL][/QUOTE]there is also one of these :smile:

Lord Julius vs. TJAOI
 

I'm surprised that Lord Julius is finding so many TF1-61 factors when I was of the understanding that TJAOI systematically churned through every exponent and every bit level up to 67.

[QUOTE=petrw1;601358]I'm surprised that Lord Julius is finding so many TF1-61 factors when I was of the understanding that TJAOI systematically churned through every exponent and every bit level up to 67.[/QUOTE]Can you point to an example(s) of a *new* factor that LJ found?

[QUOTE=James Heinrich;601365]Can you point to an example(s) of a *new* factor that LJ found?[/QUOTE]

My bad. Never mind.
I thought only new factors were reported.

[QUOTE=petrw1;601366]My bad. Never mind.
I thought only new factors were reported.[/QUOTE]


Yep, quirk of how the system is coded/defined, but not doing GIMPS stuff for stats or credits.
Been going after TF gaps sporadically before, but with the new TF gap list making it easy to feed mfaktc just started at 100,000 and headed up!

[QUOTE=petrw1;601366]I thought only new factors were reported.[/QUOTE]Yeah, the "recently cleared" report shows factor results even if they're not new. You can see on my [URL="https://www.mersenne.ca/recentfactors.php"]New Recent Factors[/URL] page that no factors <68 bits have been found this year.

M[M]109031903[/M] has a 168-bit composite factor: 363837089775240211801734278322914708564840813653583 (183216050087127739855367 78 bits * 1985836336948748649699241849 91 bits).

My first composite P-1 score. Interestingly, the full composite factor could have still have been found with just B2 = B1 = 75,000; the 91-bit component could even have been found with B2 = B1 = 20,000.

Speaking of composite factors, I found this beauty some days ago:

UID: lycorn/supernova, M13651679 has a factor: 3472625743771127990613030299559770254509858718433711042922231204290885145343 (P-1, B1=1350000, B2=3789310980)

[B]250.941[/B] bits. And:

Composite factor 3472625743771127990613030299559770254509858718433711042922231204290885145343 can be split into:
503052987459241976394793
1034412296803300959988489
6673452496002985441495464559

It´s the largest factor I´ve ever found , and the first time I find a composite factor that can be split in 3 factors

[QUOTE=lycorn;601499]It´s the largest factor I´ve ever found , and the first time I find a composite factor that can be split in 3 factors[/QUOTE]Congrats!

Strangely I noticed yesterday that [i]masser[/i] found this:[quote][M]M27893851[/M] has a 249.057-bit (75-digit) [b]composite[/b] (P23+P25+P28) factor: (P-1,B1=200000,B2=49465920)
[url=https://www.mersenne.ca/M27893851]941344976147070466133432421660342333953351560323526566733652692476498510073[/url][/quote]Very similar to yours (but [i]slightly[/i] smaller).

[QUOTE]M155999197 has a factor: 53236981495334776332913 [TF:74:77:mfaktc 0.21 barrett77_mul32_gs][/QUOTE]

It is not much, but it is something.

[M]M109080229[/M] has a 175.051-bit (53-digit) [b]composite[/b] (P24+P30) factor: [url=https://www.mersenne.ca/M109080229]49601681225870900572877780170741524727555462264509913[/url] (P-1,B1=818000,B2=35245000)

[M]M15122501[/M] has a factor: 19417184783570704930702131492084799775494055312713 (50 digits, 163.732 bits)

Nice. Huge one.

[QUOTE=Luminescence;601663][M]M15122501[/M] has a factor: 19417184783570704930702131492084799775494055312713 (50 digits, 163.732 bits)
Nice. Huge one.[/QUOTE]That's the [url=https://www.mersenne.ca/userfactors/pm1/1/bits]second-biggest P-1 factor[/url] ever!

:bow wave:

[QUOTE=James Heinrich;601665]That's the [url=https://www.mersenne.ca/userfactors/pm1/1/bits]second-biggest P-1 factor[/url] ever!

:bow wave:[/QUOTE]

I just noticed.:jvang:

I was just getting a little frustrated with this range. Not alot of factors overall

[QUOTE=Luminescence;601663][M]M15122501[/M] has a factor: 19417184783570704930702131492084799775494055312713 (50 digits, 163.732 bits)

Nice. Huge one.[/QUOTE]

Well done. Very smooth too!

How was this missed by firejuggler?
 

[url]https://www.mersenne.org/report_exponent/?exp_lo=14632711&full=1[/url]

K=2^3 × 3 × 17 × 43 × 349 × 2393 × 2827673

This is in no way a criticism of firejuggler but a question about the reliability of either the software or hardware.

hmmm here is my mE632711 file to see if there was any problem. It was the first 14.6M exponent I did.


I just redid it and I found the factor.

there is about 30 NF pm1 with the b1=800k and b2=179434710.
I'll rerun them

[QUOTE=firejuggler;601843]there is about 30 NF pm1 with the b1=800k and b2=179434710.
I'll rerun them[/QUOTE]

You may not have to .
I have a computer that due to a cranial malfunction is running P1 in 14.6.
I've already redone a few of your 800000s.
I'm away for 12 more days so I can't stop it unless I can talk my son into it.

Thank you. I'll let your computer do the job.

[M]M108320761[/M] has a factor: 60009555748293413447823073
(85.633 bits, k= 2^4 × 3^2 × 2531 × 412637 × 1841857, found by V30.8b11 with B1=463000, B2=40465194)
Which cleared 108.3M out.

[QUOTE=Zhangrc;601933][M]M108320761[/M] has a factor: 60009555748293413447823073
(85.633 bits, k= 2^4 × 3^2 × 2531 × 412637 × 1841857, found by V30.8b11 with B1=463000, B2=40465194)
Which cleared 108.3M out.[/QUOTE]

Yeah!
Good work

I've found three 100+ bits factors yesterday! (the first one is the biggest one I've found so far :smile:) Out of a total of 6 factors found yesterday in this range, and 4 so far today.
108.509 bits 461809633522436002942667757126991
105.164 bits 45433175071599793822345482321409
and 101.612 bits 3876227996028611127615928931137

[QUOTE=lisanderke;602076]I've found three 100+ bits factors yesterday! (the first one is the biggest one I've found so far :smile:) Out of a total of 6 factors found yesterday in this range, and 4 so far today.
108.509 bits 461809633522436002942667757126991
105.164 bits 45433175071599793822345482321409
and 101.612 bits 3876227996028611127615928931137[/QUOTE]

All prime factors. Exponents 397849, 397921, and 397763 respectively. Nice!

P-1 found a factor in stage #2, B1=470000, B2=13239000.
UID: Jwb52z/Clay, M111561421 has a factor: 292165419952881010847303 (P-1, B1=470000, B2=13239000)

77.951 bits.

P-1 found a factor in stage #2, B1=5550000, B2=25042991610.
UID: lisander/Desktop, M264577 has a factor: 2402275378448533966401395387089 (P-1, B1=5550000, B2=25042991610)

100.922 bits,

P-1 found a factor in stage #2, B1=5550000, B2=25042991610.
UID: lisander/Desktop, M264949 has a factor: 6338247571356035076996173356273 (P-1, B1=5550000, B2=25042991610)

102.322 bits and

P-1 found a factor in stage #2, B1=5550000, B2=25042991610.
UID: lisander/Desktop, M265261 has a factor: 20805253139081811010440552183169 (P-1, B1=5550000, B2=25042991610)

104.037 bits!

Today I keep getting bigger factors! The second one marks my biggest P-1 factor found result yet :D

P-1 found a factor in stage #2, B1=5550000, B2=22789551330.
UID: lisander/Desktop, M270587 has a factor: 11390997669503257588498195779889 (P-1, B1=5550000, B2=22789551330)

103.168 bits and

P-1 found a factor in stage #2, B1=5550000, B2=25042991610.
UID: lisander/Desktop, M267803 has a factor: 2453115957213008539833758634913543 (P-1, B1=5550000, B2=25042991610)

110.918 bits!

[M]M111744023[/M] has a 90.093-bit (28-digit) factor: [url=https://www.mersenne.ca/M111744023]1320668811711078898367468881[/url] (P-1,B1=510000,B2=18454000)

Not that exciting, but I wanted to share [B]something[/B] :grin:

M19414627 has a factor: 259213687242140687678761255384193 (107.676 bits)

My largest factor in the last few months and it was found in stage 1 with B1=800,000!

P-1 found a factor in stage #2, B1=474000, B2=13535000.
UID: Jwb52z/Clay, M113023661 has a factor: 1708323868535427894994746353 (P-1, B1=474000, B2=13535000)

90.465 bits.

P-1 found a factor in stage 1
 

[M]113076559[/M]

B1=1230000, 229904281138151649356554790047, 97.537 bits.

3 consecutive P-1 factors from same PC
 

Speck 14722069 F-PM1 2022-04-03 00:42 0.0 Factor: 350629376069681599185084001 / (P-1, B1=1700000, B2=616212870) 27.8934
Speck 14722031 F-PM1 2022-04-02 22:31 0.0 Factor: 7249170428405224821889 / (P-1, B1=1700000, B2=616212870) 27.8934
Speck 14719489 F-PM1 2022-04-02 20:20 0.0 Factor: 7636005682848927790894801 / (P-1, B1=1700000, B2=616212870) 27.8934

This is from GMP-ECM, and an error on my part:

[CODE]********** Factor found in step 2: 223
2022-04-04 09:43:03.243 Found prime factor of 3 digits: 223
2022-04-04 09:43:03.243 Composite cofactor (2^7363-1)/223 has 2215 digits[/CODE]

This is for M7363 which does not appear in any database I can find. I had intended M4363. Make of it what you will.

[QUOTE=storm5510;603269]This is for M7363 which does not appear in any database I can find.[/QUOTE]7363 is not prime, therefore it's not a Mersenne number.

[QUOTE=storm5510;603269]This is for M7363 which does not appear in any database I can find.[/QUOTE]

There are already some factors of this number noted in [URL="http://factordb.com/index.php?query=2%5E7363-1"]FactorDB[/URL].

This is a nice one:

[M]M113334241[/M] has a 112.193-bit (34-digit) factor: [url=https://www.mersenne.ca/M113334241]5936815441525476391128324308118983[/url] (P-1,B1=551000,B2=21185000)

[QUOTE=James Heinrich;603270]7363 is not prime, therefore it's not a Mersenne number.[/QUOTE]

Of course it's not prime. All the ECM exponents in the GIMPS database with found factors are not prime either. That section should not exist.

[U]Edit[/U]: I think you meant to say it is not a natural prime. Without the "2^" and "-1" it has two factors. 37 and 199.

[QUOTE=storm5510;603282]Of course it's not prime. All the ECM exponents in the GIMPS database with found factors are not prime either. That section should not exist.

[U]Edit[/U]: I think you meant to say it is not a natural prime. Without the "2^" and "-1" it has two factors. 37 and 199.[/QUOTE]

7363 itself is not prime: 7363 = 37*199.

It IS still a Mersenne Number which are all 2[SUP]n[/SUP]-1 for integer n: [url]https://mathworld.wolfram.com/MersenneNumber.html[/url]

BUT it is not a Mersenne Number that GIMPS cares about, since only those with prime exponents have a chance to be a Mersenne Prime, that is why it is not in the databases.
[url]https://www.mersenne.org/report_exponent/?exp_lo=7300&exp_hi=7400&text=1[/url]

Finally got my first Top 10 P-1 factor! :toot:
[M]M239119[/M] has a 157.217-bit (48-digit) factor: [url=https://www.mersenne.ca/M239119]212381331667662033847003656413805352059577410799[/url] (P-1,B1=30000000,B2=10120247026890)
k = 3 × 71 × 5,573 × 79,999 × 830,887 × 1,653,749 × 5,047,213 × 674,304,195,209

[QUOTE=kruoli;603319]Finally got my first Top 10 P-1 factor! :toot:[/QUOTE]Congrats!
Your new factor coincidentally also pushes my best-ever result out of the top-200 :ermm:

[QUOTE=kruoli;603319]Finally got my first Top 10 P-1 factor! :toot:
[M]M239119[/M] has a 157.217-bit (48-digit) factor: [url=https://www.mersenne.ca/M239119]212381331667662033847003656413805352059577410799[/url] (P-1,B1=30000000,B2=10120247026890)
k = 3 × 71 × 5,573 × 79,999 × 830,887 × 1,653,749 × 5,047,213 × 674,304,195,209[/QUOTE]

Excellent find!

P-1 auto-assigned by PrimeNet. [I]Prime95 v29.8 B6[/I]

M113476799: Factor: 435875148110816983338962773598903 / (P-1, B1=515000, B2=8368750)

[QUOTE=storm5510;603499]Prime95 v29.8 B6[/QUOTE]Why so old?

[QUOTE=James Heinrich;603502]Why so old?[/QUOTE]

I am glad you ask this question. On my older systems, 29.x outperforms 30.x. I never run PRP's or certification work. If I don't use it, then I don't need the capability. I sometimes use a 6.x version of [I]gpuOwl[/I] for P-1's, but it is not self-tending like [I]Prime95[/I] is. It is one less thing I have to keep up with.

[QUOTE=storm5510;603541]On my older systems, 29.x outperforms 30.x[/QUOTE]I can't comment to other worktypes, but this is absolutely untrue for P-1. v30.8 has made absolutely huge gains in P-1 performance. Do not judge it by how fast it runs, but by the bounds and probability it can achieve. Please don't do P-1 badly, you'll miss factors unnecessarily and (if done badly enough) people may need to re-do your work, which is the definition of inefficient.

[QUOTE=James Heinrich;603545]..Please don't do P-1 badly, you'll miss factors unnecessarily and (if done badly enough) people may need to re-do your work, which is the definition of inefficient.[/QUOTE]

[I]Prime95[/I] establishes its own P-1 and ECM bounds and I don't change them. If there is a difference between v29 and v30, I am unaware of it. I have no intention of doing anything "badly." This would be unnecessary work for someone else. I don't what that!

[QUOTE=storm5510;603567]If there is a difference between v29 and v30, I am unaware of it.[/QUOTE]There is. A huge difference. Since you posted about this in the v30.8 thread I assume you have been reading about it and are aware of the differences. In short, v30.8 can work with [i]significantly[/i] higher bounds for [i]significantly[/i] higher chance of factor for the same amount of allocated RAM.

[QUOTE=James Heinrich;603568]There is. A huge difference. Since you posted about this in the v30.8 thread I assume you have been reading about it and are aware of the differences. In short, v30.8 can work with [i]significantly[/i] higher bounds for [i]significantly[/i] higher chance of factor for the same amount of allocated RAM.[/QUOTE]

I have 30.8 installed on two machines but have not been using it. I will give it another look.

Found two factors for a TWOK candidate. one factor in stage one, one factor in stage two.
Both were missed by a 2003 P-1; both could be found with small B1, B2 so the large B2 from 30.8 was a little unnecessary.

[M]19442623[/M] has a 82-bit (25-digit) factor: [url=https://www.mersenne.ca/M19442623]7705180804505006995733009[/url] (P-1,B1=800000)
[M]19442623[/M] has a 78-bit (24-digit) factor: [url=https://www.mersenne.ca/M19442623]152612436387610563716369[/url] (P-1,B1=800000,B2=802202310)

Composite factor
 

[M]112084657[/M]

P-1 found a 238-bit composite factor(B1=824000, B2=242053350).

[URL="https://www.mersenne.ca/factor/408942596393398983090401"]408942596393398983090401[/URL] - 78.436bits
[URL="https://www.mersenne.ca/factor/1600346782413225832691898697103973353256067499521"]1600346782413225832691898697103973353256067499521[/URL] - 160.131bits

[QUOTE=Jan S;604448][URL="https://www.mersenne.ca/factor/1600346782413225832691898697103973353256067499521"]1600346782413225832691898697103973353256067499521[/URL] - 160.131bits[/QUOTE]That is a top 5 all time P-1 factor. Congrats!!

[QUOTE=Jan S;604448][M]112084657[/M]

P-1 found a 238-bit composite factor(B1=824000, B2=242053350).

[URL="https://www.mersenne.ca/factor/408942596393398983090401"]408942596393398983090401[/URL] - 78.436bits
[URL="https://www.mersenne.ca/factor/1600346782413225832691898697103973353256067499521"]1600346782413225832691898697103973353256067499521[/URL] - 160.131bits[/QUOTE]

Impressive - nice find!

[QUOTE=Uncwilly;604449]That [STRIKE]is[/STRIKE] would have been* a top 5 all time P-1 factor. Congrats!![/QUOTE]
Would have been if it were prime.
Composite factors' sizes are arbitrarily large and don't count.

[QUOTE=lycorn;601499]Speaking of composite factors, I found this beauty some days ago:

UID: lycorn/supernova, ...[/QUOTE]

[QUOTE=Batalov;604480]Would have been if it were prime.[/QUOTE]No, just the 160-bit prime component of the composite factor is #5 on the [URL="https://www.mersenne.ca/userfactors/pm1/1/bits"]biggest P-1 Mersenne Factors list[/URL].

Ah, ok.
That message said "a top 5 all time P-1 factor" (period). I know a thing or two about top all time P-1 factors - they are [URL="https://members.loria.fr/PZimmermann/records/Pminus1.html"]way larger[/URL].

P-1 found a factor in stage #2, B1=490000, B2=13987000.
UID: Jwb52z/Clay, M114782309 has a factor: 274973054029559054066929 (P-1, B1=490000, B2=13987000)

77.864 bits.

When looking at this result, I was expecting it to be yet another composite factor. Turns out it wasn't:

[M]M12731681[/M] has a 151.792-bit (46-digit) factor: [URL="https://www.mersenne.ca/M12731681"]4942614515973735792916302243662188576877302039[/URL] (P-1,B1=400000,B2=428459850)

That will be 17th place on the [URL="https://www.mersenne.ca/userfactors/pm1/1/bits"]Mersenne top factors for P-1[/URL] and is by far the biggest factor I ever found with P-1! :big grin:

Whaaa! Congrats! Nice found!
Same number of digits like my best (currently position 13), but it falls about 0.9 bits shorter :razz:

Getting lucky again with my P-1 factoring:

[M]M12782851[/M] has a 235.159-bit (71-digit) [B]composite[/B] (P21+P24+P27) factor: [URL="https://www.mersenne.ca/M12782851"]61645213700098762638579831947213762951673986053039553206940532463429217[/URL] (P-1,B1=400000,B2=428459850)

That's the biggest triple factor I ever found (out of 4 in total).

P-1 found a factor in stage #1, B1=509000.
UID: Jwb52z/Clay, M115285087 has a factor: 111450819426998736215606681 (P-1, B1=509000)

86.527 bits.

I finally found one that made the top 500 in this list [url]https://www.mersenne.ca/userfactors/pm1/1/bits[/url].

[url]https://www.mersenne.ca/exponent/3884411[/url] has a 123.607 bit exponent.

currently at #384 and the first factor I have found larger than 109 bits!

[QUOTE=DrobinsonPE;605923]...the first factor I have found larger than 109 bits![/QUOTE]But according to your [url=https://www.mersenne.ca/userfactors/pm1/82293/bits]personal factors list[/url], you've found this and 4 other factors larger than 109.x bits, including two larger than this (131 & 136 bits, #84 & #158 in the top-500 list).

[QUOTE=James Heinrich;605924]But according to your [url=https://www.mersenne.ca/userfactors/pm1/82293/bits]personal factors list[/url], you've found this and 4 other factors larger than 109.x bits, including two larger than this (131 & 136 bits, #84 & #158 in the top-500 list).[/QUOTE]

Cool! I did not know that list existed. I was just watching the factors I found and keeping track in my head. Obviously i missed a few and found some before I started looking.

You are my new favorite person for today!

[QUOTE=James Heinrich;605924]But according to your [URL="https://www.mersenne.ca/userfactors/pm1/82293/bits"]personal factors list[/URL], ...[/QUOTE]


Hi James. Are you the right person to ask about merging my two IDs as shown on that list (the old "Lord Julius" into newer "LordJulius")? If it's simple, I would appreciate it.

[QUOTE=LordJulius;605965]Hi James. Are you the right person to ask about merging my two IDs as shown on that list (the old "Lord Julius" into newer "LordJulius")? If it's simple, I would appreciate it.[/QUOTE]I am the right person to ask about anything on mersenne.ca :smile:
I have renamed/merged all [c]Lord Julius[/c] into [c]LordJulius[/c].

P-1 found a factor in stage #1, B1=510000.
UID: Jwb52z/Clay, M115435169 has a factor: 12873265828509838756458407 (P-1, B1=510000)

83.413 bits.

[M]M110368889[/M] has a 119.453-bit (36-digit) factor: [url=https://www.mersenne.ca/M110368889]909751501112745686529881562093681577[/url] (P-1,B1=585000,B2=34699170)

one of my older machines still working hard...