P-1 found a factor in stage #2, B1=685000, B2=12501250.
UID: Jwb52z/Clay, M86261069 has a factor: 108347656269103560321473 (P-1, B1=685000, B2=12501250)

76.520 bits.

Another one under 1M:

lycorn/asteroid, M[B]292717[/B] has a factor: [B]3767709660056805735113918599207[/B] (ECM curve 86, B1=350000, B2=25000000)

101.57 bits

k = 3[SUP]2[/SUP] × 293 × 94302613 × 25880080988239

Definitely not suitable for TF or P-1...

I didn't report here, but

ET_/Pentium_G2030, M2493949 has a factor: 8999652246905381346333863 (ECM curve 137, B1=50000, B2=5000000)

82.896 bits

k = 11 × 101 × 1624030217121929

M2504969 - 88 bits
 

ECM found a factor in curve #1, stage #2

Sigma=394033186513377, B1=50000, B2=5000000.

M2504969 has a factor: 312774689772122552706712063

ECM curve 1, B1=50000, B2=5000000

And another one...

UID: lycorn/asteroid, M701179 has a factor: 62175023660062474016743 (ECM curve 23, B1=250000, B2=25000000)

[B]75.719[/B] bits

This one had been missed @ B1=50,000.

What is the largest [smallest factor of a Mersenne-Pseudoprime (the ones with prime exponents) ] ever found?

To clarify, looking for the equivalents of 23 and not 89 or 2047 for M11 of any Mersenne-Pseudoprime which is the largest ever found.
Thanks in advance.

[QUOTE=a1call;482102]What is the largest [smallest factor of a Mersenne-Pseudoprime (the ones with prime exponents) ] ever found?

To clarify, looking for the equivalents of 23 and not 89 or 2047 for M11 of any Mersenne-Pseudoprime which is the largest ever found.
Thanks in advance.[/QUOTE]

Have a look in here: [url]https://eprint.iacr.org/2014/653.pdf[/url]

[QUOTE=VBCurtis;482119]Have a look in here: [URL]https://eprint.iacr.org/2014/653.pdf[/URL][/QUOTE]

Thank you VBCurtis.

I did not get result from that link.

Some of the 17 exponents are not prime. The ones that are and I checked, report enormous factors of Mersennes with also much smaller factors such as:


[URL]https://www.mersenne.org/report_exponent/?exp_lo=1129&exp_hi=[/URL]

Thanks for the reply though.:smile:

ETA the largest, smallest factor seems to be here (from the list of 17)
[url]https://www.mersenne.org/report_exponent/?exp_lo=1123&exp_hi=[/url]

I doubt that is the largest ever found.

Ah, sorry; I was thinking of "largest penultimate", rather than largest smallest-factor.
I queried factordb; 2^727-1 has P98, while 2^1061-1 has P143. I searched up to 1200, since no SNFS has been done above 1200 and ECM can't find factors over P90 (well, hasn't yet done so!).

[QUOTE=VBCurtis;482129]Ah, sorry; I was thinking of "largest penultimate", rather than largest smallest-factor.
I queried factordb; 2^727-1 has P98, while 2^1061-1 has P143. I searched up to 1200, since no SNFS has been done above 1200 and ECM can't find factors over P90 (well, hasn't yet done so!).[/QUOTE]

Wow, thank you very much sir.
Wished I knew how to do the search myself.
Sorry for my nonmathematician ignorance, but which method has factored M1061? is that SNFS?

"LL verified factored"
Are they factored using LL test?

Let p=2618163402417 * 2^1290000-1

Let q=2*p+1 = 2618163402417 * 2^1290001-1

Both p&q are prime, and q | Mp ([url]http://primes.utm.edu/top20/page.php?id=2[/url])

That's kind of like starting with a factor and finding a product thing. Without a limit on the upper bound of the exponents, there can be very large factors (reverse) found.
My main interest was knowing which factorization method was likely to yield result for smallish exponents such as 1277.
Thank you for all the replies.

Still, that's a very big factor.:smile:

More to follow, I hope,

UID: lycorn/asteroid, M[B]701279[/B] has a factor: [B]109524525600903796107001439[/B] (ECM curve 6, B1=250000, B2=25000000),

k = 7 × 89459 × 124700579539997

86.5 bits

I ran P-1 for [URL="https://www.mersenne.org/report_exponent/?exp_lo=2348581&full=1"]M2348581[/URL] with B1 = 500000, B2 = 15M and the computer found the factor 5548683844149279840865697.

k = 2[sup]4[/sup] × 269 × 391057 × [b]701846461[/b]

The largest prime factor of k is 46.8 times greater than B2.

Early this morning:

UID: lycorn/asteroid, [B]M701837[/B] has a factor: [B]259854790206125142269983759[/B] (ECM curve 143, B1=250000, B2=25000000),

k =3 × 3653737 × 16889077695097

87.7 bits

P-1 found a factor in stage #1, B1=695000.
UID: Jwb52z/Clay, M86793739 has a factor: 910549085913587826291193 (P-1, B1=695000)

79.591 bits.

P-1 found a factor in stage #2, B1=695000, B2=12683750.
UID: Jwb52z/Clay, M86799803 has a factor: 1192325946520069040995537 (P-1, B1=695000, B2=12683750)

79.980 bits.

P-1 found a factor in stage #1, B1=675000.
UID: Jwb52z/Clay, M85739737 has a factor: 679361995807826610400111 (P-1, B1=675000)

79.169 bits.

Sometimes aliquot factoring can give you a nice rush of blood to the head for a second:

[CODE]GMP-ECM 7.0.4 [configured with GMP 6.1.2, --enable-asm-redc] [ECM]
Input number is 1517439814201108887897934862271262558104534535301883255672348462116670999816566813931054817374035671332731471319464058197572039195388873161 (139 digits)
Using B1=110000000, B2=776278396540, polynomial Dickson(30), sigma=1:2976032775
Step 1 took 207818ms
Step 2 took 81363ms
********** Factor found in step 2: 10480969962437176114024058906626759361702940245272292968255351471223212992493
Found [SPOILER]composite[/SPOILER] factor of 77 digits: 10480969962437176114024058906626759361702940245272292968255351471223212992493
Prime cofactor 144780475436860556690897274398404208790676771300263567589078477 has 63 digits[/CODE]

Nothing to write home about, of course, but a nice rush while grepping output files for "found"... :rolleyes:

I found factor: 10954941885802061514527896888954730695799694887 (M42727 - ECM curve 189, B1=3000000, B2=300000000) 152.940 bits - 47 digits :fusion:

Not as flashy as yours :bow:, but a new one just popped up. One less to go...


UID: lycorn/asteroid, M[B]502141[/B] has a factor: [B]7507285166367433962860321[/B] (ECM curve 70, B1=250000, B2=25000000)

82.6 bits

k = 24 × 5 × 296269 × 315392263213

[QUOTE=Miszka;486146]I found factor: 152.940 bits [/QUOTE]

Nice one!!

[URL="https://www.mersenne.org/report_exponent/?exp_lo=87297169&exp_hi=&full=1"] M87297169[/URL] has a factor: 42094798243921532482960513482130070610271580522731637977 - 184.780 bits (P-1, B1=705000, B2=13218750, E=12)

Composite (84.996 + 99.783 bits) of course.

After over 3 weeks without new factors, I got two factors for the same number within 24 hours:

M27067 has a factor: 15021033803699159980877285173903129 (ECM curve 306, B1=3000000, B2=300000000)
M27067 has a factor: 559863370256975086095817920861703 (ECM curve 161, B1=3000000, B2=300000000)

108.8 and 113.5 bits / 33 and 35 digits

Sorry for being offtopic, but i'd like to avoid stepping on someone's toes by doing ECM on the same exponents;

Is the user James Hintz also in this forum?

[QUOTE=heliosh;487199]Sorry for being offtopic, but i'd like to avoid stepping on someone's toes by doing ECM on the same exponents;

Is the user James Hintz also in this forum?[/QUOTE]

I believe his forum username is WVU Mersenneer.

[QUOTE=heliosh;487199]Sorry for being offtopic, but i'd like to avoid stepping on someone's toes by doing ECM on the same exponents;

Is the user James Hintz also in this forum?[/QUOTE]

ECM does not result in toe stepping. Because of the way it generates a random curve any number of people can ECM the same number without concern

Yes, but when I'm doing all curves of a B1 size and someone else is doing the same, it's a waste of CPU time since the gain of additional curves is negligible.


The server doesn't know that I'm doing all curves, so it still allows assignments for the same exponent and B1 size.
For example:
[url]https://www.mersenne.org/report_exponent/?exp_lo=8837&full=1[/url]

ah... but no... see if you do more curve it can be *added* to make the next level... Ie : 4 time the nessecary number of curve for a 55 digit test is equivalent of 1 full amount of curve for a 60 digit test

[QUOTE=heliosh;487268]The server doesn't know that I'm doing all curves[/QUOTE]

Well, then, let it know by periodically reporting curve counts. Anyway, don't worry about minor inefficiencies. Let the system do its thing.

Fondue a factor
 

Ok then, back to topic.


M8929 has a new factor: 1115430961341245177793296572392840751 / (ECM curve 777, B1=3000000, B2=300000000)
37 digits, 119.747 bits

[QUOTE=heliosh;487268]The server doesn't know that I'm doing all curves, [...] [/QUOTE]
Which, essentially, is the root of all evil. If you're running thousands of curves on an exponent, don't reserve only 150 curves.

Reserving the actual number of curves you'll be running would make it much easier for [I]everyone else[/I] not to step on [I]your[/I] toes.

James, me, and most others who run thousands of curves (especially all remaining ones) will usually do exactly that, as well as check how many curves are being run on an exponent by other people. And that has worked out fine for years now...

Sounds reasonable.

P-1 found a factor in stage #2, B1=705000, B2=12866250.
UID: Jwb52z/Clay, M87663241 has a factor: 3684639673975304433875891200441 (P-1, B1=705000, B2=12866250),

101.539 bits.

UID: lycorn/asteroid, [B]M509513[/B] has a factor:[B]32938833110244022629041285311[/B] (ECM curve 42, B1=250000, B2=25000000)

94.734 bits

k = 3 × 5 × 7 × 61 × 521190323 × 9682945049

UID: ET_/Imac, M86374747 has a factor: 1714361122821964709562404951 / (P-1, B1=700000, B2=13650000, E=12)

P-1 found a factor in stage #2, B1=700000, B2=12775000.
UID: Jwb52z/Clay, M87222229 has a factor: 174466303146501293028631 (P-1, B1=700000, B2=12775000)

77.207 bits.

I ran ECM with B1=3e6 on 105 exponents from M8831 to M9973.
These factors were found:
M8929 1115430961341245177793296572392840751 (ECM curve 777)
M8963 12102907522238912136363264325152257671 (ECM curve 94)
M9043 1214227396319818076542537632130381319 (ECM curve 1944)
M9241 42833623397271509550058451923527601 (ECM curve 154)
M9323 1333520398848362959146986064051807672224671 (ECM curve 3075)
M9539 223212586274489597961708131344467984319 (ECM curve 244)
M9539 539739762366037934978545147421430377 (ECM curve 195)
M9833 489061585821401691783649055431739696807 (ECM curve 932)
M9883 450826387535591546789201943375206602903 (ECM curve 2170)

[QUOTE=heliosh;490708]I ran ECM with B1=3e6 on 105 exponents from M8831 to M9973.
These factors were found:
M8929 1115430961341245177793296572392840751 (ECM curve 777)
M8963 12102907522238912136363264325152257671 (ECM curve 94)
M9043 1214227396319818076542537632130381319 (ECM curve 1944)
M9241 42833623397271509550058451923527601 (ECM curve 154)
M9323 1333520398848362959146986064051807672224671 (ECM curve 3075)
M9539 223212586274489597961708131344467984319 (ECM curve 244)
M9539 539739762366037934978545147421430377 (ECM curve 195)
M9833 489061585821401691783649055431739696807 (ECM curve 932)
M9883 450826387535591546789201943375206602903 (ECM curve 2170)[/QUOTE]

Cool....maybe you can have the same luck with some small exponents with NO factors yet.

I'd have to buy more luck for that, to avoid getting bored.

[URL="https://www.mersenne.org/report_exponent/?exp_lo=31817&full=1"]M31817[/URL] has some factors:

312876296180312279168622885407233 discovered 2018-[B]05-29[/B] by kkmrkkblmbrbk
61616511924264545425643699355785809 discoverd 2018-[B]05-30[/B] by kkmrkkblmbrbk
265196408951138298839977855543644017 discovered 2018-[B]05-30[/B] by me
24120390327081671517843130891211537004871 discoverd [B]today[/B] by me


That's 4 new factors >100 bits in 2 months. Together with the previously known ones, that's a total of [URL="http://www.mersenne.ca/manyfactors.php"]9 known factors[/URL].

[QUOTE=nordi;492226][URL="https://www.mersenne.org/report_exponent/?exp_lo=31817&full=1"]M31817[/URL] has some factors:

312876296180312279168622885407233 discovered 2018-[B]05-29[/B] by kkmrkkblmbrbk
61616511924264545425643699355785809 discoverd 2018-[B]05-30[/B] by kkmrkkblmbrbk
265196408951138298839977855543644017 discovered 2018-[B]05-30[/B] by me
24120390327081671517843130891211537004871 discoverd [B]today[/B] by me


That's 4 new factors >100 bits in 2 months. Together with the previously known ones, that's a total of [URL="http://www.mersenne.ca/manyfactors.php"]9 known factors[/URL].[/QUOTE]


Remaining cofactor is composite. Anyway, nice factors. :smile:

P-1 found a factor in stage #2, B1=710000, B2=12957500.
UID: Jwb52z/Clay, M88182361 has a factor: 261097855288862092613113 (P-1, B1=710000, B2=12957500)

77.789 bits.

Seems we missed a very small factor.
 

[url]www.mersenne.org/report_exponent/?exp_lo=32077&full=1[/url]

Even TJAOI missed it

Why do you think that's a new factor? It's been known since the before-time (there is no date associated with it in my data, so it's at least older than 2012).
Three PRP tests were done in 2017-Sep with that as a known factor.

[QUOTE=James Heinrich;493155]Why do you think that's a new factor? It's been known since the before-time (there is no date associated with it in my data, so it's at least older than 2012).
Three PRP tests were done in 2017-Sep with that as a known factor.[/QUOTE]

I ASS-umed it was new because ANONYMOUS reported it today.

Incidentally, impossibly high B2 ?!

[QUOTE=axn;493187]Incidentally, impossibly high B2 ?![/QUOTE]Probably not coincidentally, that B2 value is 2[sup]64[/sup]. How or why I don't know, but it's not a storage-regurgitation error, that's the B2 value in the submitted result line. The result line also contains a user/computer ID, and an assignment ID, I'm not sure why the result was submitted anonymously.

[QUOTE=James Heinrich;493190]Probably not coincidentally, that B2 value is 2[sup]64[/sup]. How or why I don't know, but it's not a storage-regurgitation error, that's the B2 value in the submitted result line. The result line also contains a user/computer ID, and an assignment ID, I'm not sure why the result was submitted anonymously.[/QUOTE]

Anyway, they are the all time leader now. And all the production stats are f'ed up.

The first p-1 factor found by my hardware, after 72 unsuccessful attempts.
[QUOTE]Factor: 1645517559786763250768607073 / (P-1, B1=760000, B2=760000, e=12, n=5184K CUDAPm1 v0.20)[/QUOTE]
90 bits!

[QUOTE=penlu;493938]...
Factor: 1645517559786763250768607073 / (P-1, B1=760000, B2=760000, e=12, n=5184K CUDAPm1 v0.20)
...
[/QUOTE]B1=B2 and E=12 ? ? ? !
1645517559786763250768607073 - 1 = 2^5 × 3^3 × 19 × 31 × 269 × 319351 × 427351 × 88078153
The factor was found in stage 1 so the Brent Sumaya extension did not come into play. CUDAPm1 brags about a E=12 that did not come into play :-(

Jacob

[URL="http://www.mersenne.ca/brent-suyama.php"]mersenne.ca isn't taken by these shenanigans[/URL] :) 88,078,153 isn't listed there

But also note that the P-1 effort isn't registered on mersenne.ca yet either (will appear sometime after midnight GMT during the nightly sync)
[url]http://www.mersenne.ca/exponent/88078153[/url]

[QUOTE=S485122;493951]B1=B2 and E=12 ? ? ? !
1645517559786763250768607073 - 1 = 2^5 × 3^3 × 19 × 31 × 269 × 319351 × 427351 × 88078153
The factor was found in stage 1 so the Brent Sumaya extension did not come into play. CUDAPm1 brags about a E=12 that did not come into play :-(

Jacob[/QUOTE]

All factors of a Mersenne number with exponent p (prime) can be expressed as 2*k*p+1.

In your case 88078153 equals p, so k = 2[SUP]4[/SUP] × 3[SUP]3[/SUP] × 19 × 31 × 269 × 319351 × 427351.

All prime factors of k are less than the bound B1, So, there is nothing special about this factorization using P-1.

[QUOTE=alpertron;494208]So, there is nothing special about this factorization using P-1.[/QUOTE]

It's special to me because it's my first :'(

I found a factor 7235281275265153693689909724758049 of M91943, which is the first my hardware has found using ECM.

[QUOTE=penlu;494353]It's special to me because it's my first :'(

I found a factor 7235281275265153693689909724758049 of M91943, which is the first my hardware has found using ECM.[/QUOTE]

:tu:

Another one only fit for ECM:


Exponent: [B]183713[/B]
Factor: 159739685774531509548162186329
[B]97.012[/B] bits
k = 2[SUP]2[/SUP] × 13[SUP]2[/SUP] × 643126263022633956403

P-1 found a factor in stage #1, B1=715000.
UID: Jwb52z/Clay, M88737373 has a factor: 547048396504106740832234647 (P-1, B1=715000),

88.822 bits.

P-1 found a factor in stage #1, B1=715000.
UID: Jwb52z/Clay, M88801717 has a factor: 863225712976878887075783713 (P-1, B1=715000

89.480 bits.

phoned a factor...
 

... and I got this pretty one:
[CODE]UID: RU/Nomad2C, M12103879 has a factor: 76589819640254233618412004377777346859019502009144302474620595280120616202419586537 (P-1, B1=430000, B2=8500000, E=12)
[/CODE]

275 bits, composite (84 + 90 + 103). As a side note, had to resort to manual page submission in order to have it processed (CURL raised a timeout in automatic processing and stopped the queue).

[QUOTE=ric;497563]275 bits, composite (84 + 90 + 103)[/QUOTE]That is pretty! :bow:

P-1 found a factor in stage #2, B1=715000, B2=13048750.
UID: Jwb52z/Clay, M89067427 has a factor: 524395562032803866876089 (P-1, B1=715000, B2=13048750),

78.795 bits.

[QUOTE=ric;497563]275 bits, composite (84 + 90 + 103). As a side note, had to resort to manual page submission in order to have it processed (CURL raised a timeout in automatic processing and stopped the queue).[/QUOTE]

So what would have happened if you didn't manually intervene? The factor would have been dropped and lost?

And how often has that actually happened, to other people, and no one the wiser?

An interesting observation: here's my thinking

[QUOTE=GP2;497613] The factor would have been dropped and lost?[/QUOTE]

No.

[QUOTE=GP2;497613] So what would have happened if you didn't manually intervene?[/QUOTE]

I've opted to use Primenet to report results, so the large factor and all results following that one, they all stacked up into prime.spl (I saw this factor the day after its discovery, so this is a fact) - a message on screen [CODE]CURL library error: Operation timed out after 180000 milliseconds with 0 bytes received[/CODE] and an equivalent entry in prime.log warned that something weird was happening at each subsequent result/communication attempt - in all likelihood, with such visible warnings, even a novice user would have come to mersenneforum to ask for advice.

Had I opted for [B]not[/B] communicating directly to Primenet, the first subsequent manual submission would have lasted a bit longer than usual.

[QUOTE=GP2;497613] And how often has that actually happened, to other people, and no one the wiser?[/QUOTE]

IMAO P(x)->0 :smile:

Two side notes:[LIST=1][*]I've also pondered about asking to raise the 3 min threshold for CURL communication, but the low occurrence of these large factors IMO does not justify this measure[*]oh, and BTW I noticed that this factor does not appear in the "Recent Cleared" report, but again clipping the outliers to me is a sane measure[/LIST]
TL;DR: I like the way it is, and see no danger in it. Other opinions are welcome :smile:

I suspect that the original (automatic) submission triggered an attempt to factor the factor, which is non-trivial, and the communication timed out while waiting for the result of the factor factorization. By the time the manual communication was attempted, the original factor splitting was completed and cached so the manual communication went through immediately.

On a side note, my site now displays composite factors found as the list of the prime components for greater clarity:
[url]https://www.mersenne.ca/exponent/12103879[/url]
I also wonder why the original P-1, apparently done nearly 18 years ago, should have but didn't find two of the three factors?

[QUOTE=James Heinrich;497622]By the time the manual communication was attempted, the original factor splitting was completed and cached so the manual communication went through immediately.[/QUOTE]

It's likely, and my educated guess is that the "factor the factor" process was started during my initial manual submission (the large factor + subsequent no factor results), and completed - caching included - by the time I re-submitted the large factor alone (impatient? who, me? :smile:).

This guess of mine is based on the evidence that I have two identical result lines for it in my results report (crediting half a GHz-Day each, go figure!) and on mersenne.ca as well.

[QUOTE=James Heinrich;497622]I also wonder why the original P-1, apparently done nearly 18 years ago, should have but didn't find two of the three factors?[/QUOTE]

Not the first one of this kind, probably won't even be the last (another recent example: [URL="https://www.mersenne.ca/exponent/12076891"]M12076891[/URL] - incidentally, it has a glitch right now, preventing display).

I recall a discussion somewhere else on mersenneforum, with the general consensus that re-doing older P-1 was basically futile (and however mersenne.ca maintains [URL="https://www.mersenne.ca/p1missed.php"]this list[/URL]).

[QUOTE=ric;497627][URL="https://www.mersenne.ca/exponent/12076891"]M12076891[/URL] - incidentally, it has a glitch right now, preventing display[/QUOTE]Already fixed :smile:

[QUOTE=James Heinrich;497628]Already fixed :smile:[/QUOTE]

Amazing speed! Thx

P-1 found a factor in stage #2, B1=715000, B2=13227500.
UID: Jwb52z/Clay, M89267203 has a factor: 34165373881617506022060001 (P-1, B1=715000, B2=13227500),

84.821 bits.

P-1 found a factor in stage #1, B1=715000.
UID: Jwb52z/Clay, M89218183 has a factor: 1578944744818761269375521 (P-1, B1=715000),

80.385 bits.

This time CUDAPm1's Brent-Suyama extension actually helped!

M88729169 is split by:

[QUOTE]
Factor: 203879517521451990434959 / (P-1, B1=765000, B2=18933750, e=6, n=5184K CUDAPm1 v0.20)
[/QUOTE]

203879517521451990434959 - 1 = 2 × 3 × 7 × 107 × 113 × 4524761281 × 88729169

4524761281 / 18933750 ~ 238.98

P-1 found a factor in stage #2, B1=730000, B2=13322500.
UID: Jwb52z/Clay, M89800379 has a factor: 21299539644933319630246941103 (P-1, B1=730000, B2=13322500)

94.105 bits.

GMP-ECM
 

I have found two [U]new[/U] factors for M66301 with [I]GMP-ECM[/I] which are not on the server. It does not create a results file so I made screen captures of the pertinent areas which shows the work. I do not know what to do with them. Suggestions? :confused2:

Go to mersenne.org and make sure you are logged in with your account in the top right corner, then go to "Manual Testing - results" and paste this:

UID: user/computer, M66301 has a factor: xxxxx
UID: user/computer, M66301 has a factor: xxxxx

but change the 2 "xxxxx" to the 2 factors and "user" to your username, the one you have in Prime95 prime.txt in the line "UserID=", and change "computer" to whatever computer name you use, but it does not really matter. You can use the ID from the line "ComputerID=" in Prime95 local.txt

[QUOTE=storm5510;502179]I have found two [U]new[/U] factors for M66301 with [I]GMP-ECM[/I] which are not on the server. It does not create a results file so I made screen captures of the pertinent areas which shows the work. I do not know what to do with them. Suggestions? :confused2:[/QUOTE]

If you don't care about receiving GHz-days points, you can just go to [url]https://www.mersenne.org/manual_result/[/url] and type in

[CODE]
M66301 has a factor: nnnnnnnnnnnnnnn
M66301 has a factor: xxxxxxxxxxxxxxxxx
[/CODE]

This will credit you as the discoverer (if you are logged in) but give you basically zero GHz-days.

If you want the GHz-days, I imagine you'd probably have to contact an admin to handle it manually.

[QUOTE=storm5510;502179]I have found two [U]new[/U] factors for M66301 with [I]GMP-ECM[/I] which are not on the server. :confused2:[/QUOTE]
Make sure that the new factors are not simply products of the three known small factors.
An easy way to see those is in [URL]https://www.mersenne.ca/exponent/66301[/URL]

[QUOTE=Batalov;502192]Make sure that the new factors are not simply products of the three known small factors.
An easy way to see those is in [URL]https://www.mersenne.ca/exponent/66301[/URL][/QUOTE]

They are both composites of the three on the server.

29,698,252,545,089 and 14,728,298,367,798,007,046,809.

I am glad you made the above posting. Next time, if there is one, I will know how to check. Thank you.

:smile:

If you ever need to do a quick check if a found factor is prime or composite, for small (<46 digits) numbers you can use my site, or for numbers of any size you can use Dario's Interger Factorization Calculator (which is better in pretty much every way):
[url]https://www.mersenne.ca/factor.php[/url]
[url]https://www.alpertron.com.ar/ECM.HTM[/url]

[QUOTE=James Heinrich;502224]If you ever need to do a quick check if a found factor is prime or composite, for small (<46 digits) numbers you can use my site, or for numbers of any size you can use Dario's Interger Factorization Calculator (which is better in pretty much every way):
[URL]https://www.mersenne.ca/factor.php[/URL]
[URL]https://www.alpertron.com.ar/ECM.HTM[/URL][/QUOTE]

I have been using your site. The ones in your links do not waste any time. Thanks! :smile:

I hope I'm not stealing his thunder.....
 

Anton Repko Manual testing 4591 F-ECM 2018-12-13 07:52 0.0 3420.2395 Factor: 622304041006452740824160434864315474346236458056663 / (ECM curve 898, B1=110000000, B2=900514153782)

I did notice it too.
The sub 10K range is one step closer to be cleared (which doesn´t necessarily mean it will ever be...) :smile:

Given the amount of credit earned and the large B2 value, this one appears to have been found using GMP-ECM

[QUOTE=lycorn;502672]I did notice it too.
The sub 10K range is one step closer to be cleared (which doesn´t necessarily mean it will ever be...) :smile:
[/QUOTE]

1,229 Exponents
22 Prime = 1.79%
1,142 Factored = 92.92%
65 Remaining = 5.29%
1 Factor in the last year; 5 in the last 3 years.

P-1 found a factor in stage #2, B1=730000, B2=13505000.
UID: Jwb52z/Clay, M90073891 has a factor: 2050855691794382163177943 (P-1, B1=730000, B2=13505000)\

80.763 bits.

P-1 found a factor in stage #2, B1=730000, B2=13505000.
UID: Jwb52z/Clay, M90224503 has a factor: 2988438854649985393367591 (P-1, B1=730000, B2=13505000)

81.306 bits.

P-1 found a factor in stage #1, B1=730000.
UID: Jwb52z/Clay, M90297301 has a factor: 477501114214912796207489 (P-1, B1=730000)

78.660 bits.

M921001 has a factor.
It was found by ECM, using B1=250000, B2=25000000. Given that the size of the factor is just over 78 bits, it was missed by the previous trial @ B1=50000. It took 115 curves, tho. Oh well, one down.

[QUOTE=lycorn;505933]M921001 has a factor.
It was found by ECM, using B1=250000, B2=25000000. Given that the size of the factor is just over 78 bits, it was missed by the previous trial @ B1=50000. It took 115 curves, tho. Oh well, one down.[/QUOTE]

It is a 24-digit factor. A full t25 ECM has about 25% probability of missing such a factor (25% is a ballpark -- I don't know the exact probability).

P-1 found a factor in stage #2, B1=680000, B2=12070000.
UID: Jwb52z/Clay, M90532069 has a factor: 2470306454303834603641759 (P-1, B1=680000, B2=12070000)

81.031 bits.

P-1 found a factor in stage #2, B1=680000, B2=12070000.
UID: Jwb52z/Clay, M90387127 has a factor: 21114889399427865887545841 (P-1, B1=680000, B2=12070000)

84.126 bits.

P-1 found a factor in stage #1, B1=680000.
UID: Jwb52z/Clay, M90729377 has a factor: 35001746371256696847407311 (P-1, B1=680000)

84.856 bits.

ECM found a factor in curve #312, stage #2
Sigma=2655318244881862, B1=250000, B2=25000000.
M322939 has a factor: 11174935515705269731353543251549484660209 (ECM curve 312, B1=250000, B2=25000000)


41 digits(133.037 bits) factor was found with ECM bounds for 30-digit factors

You´ve been finding a fair amount of ECM factors for small exponents lately :bow:. I have some experience in working in those small ranges, so I truly appreciate your effort. How many cores have you assigned?

I am using 48 cores for ECM work in 320000-360000 range with a major goal to complete all unfactored <500000 to 30-digits level.
4 more cores are working on numbers with known factors in 10000-11000 range.

Right, That´s a considerable amount of computing power. Hope you´ll find many more factors along the way :smile:.
I´m working a bit further up: 600k and 800k, also with B1=250000. My success rate has been rather low, though, which is normal considering I have only 8 cores at it, and four of them belong to a 10-year old i5-750

For now 15 factors was found in ~130 attempts.
Good luck to you, too.

[QUOTE=newalex;510937]
4 more cores are working on numbers with known factors in 10000-11000 range.[/QUOTE]

Please tell me you are using GMP-ECM for stage 2.

Yes, that is good advice. For such small exponents there is a lot to gain. One of these days I will resume my "sub 10K" crusade and then I'll be using GMP-ECM once again.
After all, there are just 64 left to factorize... LOL