[M]M36919[/M] has a 180.968-bit (55-digit) factor: [URL="https://www.mersenne.ca/M36919"]2997347544642661833497896836795494793702018162645139063[/URL] (P-1,B1=2000000000,B2=401927737170960)


That gets me to the top of the [URL="https://www.mersenne.ca/userfactors/pm1/1/bits"]list of P-1 factors for Mersenne numbers[/URL]! And all thanks to the new version 30.8 of mprime.


:maybeso::wacky:

:groupwave: :party:

Nice!

Wow! Congrats!

[QUOTE=nordi;606342] That gets me to the top of the [URL="https://www.mersenne.ca/userfactors/pm1/1/bits"]list of P-1 factors for Mersenne numbers[/URL]! And all thanks to the new version 30.8 of mprime.[/QUOTE]

Congratulations!

This comes in at 10th place on the [URL="https://members.loria.fr/PZimmermann/records/Pminus1.html"]all-time P-1 list[/URL], i.e. not restricted to Mersennes. You should drop Paul Zimmermann an email; his address is on the page I linked.

[QUOTE=charybdis;606354]This comes in at 10th place on the [URL="https://members.loria.fr/PZimmermann/records/Pminus1.html"]all-time P-1 list[/URL], i.e. not restricted to Mersennes. You should drop Paul Zimmermann an email; his address is on the page I linked.[/QUOTE]Record-size Mersenne factors are automatically reported to Paul Zimmerman (and Richard Brent for ECM) during the nightly data sync. The codepath for auto-reporting P-1 factors hasn't yet been tested (nobody has found a sufficiently large P-1 factor since I wrote the code in 2020) so tonight will be its test. Wouldn't hurt for [i]nordi[/i] to email him anyways.

[QUOTE=storm5510;603269]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]Substantially beyond the limits of the 2- Cunningham table.

Don't let that stop you from trying to find more factors though.

[QUOTE=nordi;606342][M]M36919[/M] has a 180.968-bit (55-digit) factor: [URL="https://www.mersenne.ca/M36919"]2997347544642661833497896836795494793702018162645139063[/URL] (P-1,B1=2000000000,B2=401927737170960)


That gets me to the top of the [URL="https://www.mersenne.ca/userfactors/pm1/1/bits"]list of P-1 factors for Mersenne numbers[/URL]! And all thanks to the new version 30.8 of mprime.
[/QUOTE]
That is indeed a good factor!

Cross-post it in the "([I]Preying for[/I]) World Record P-1" thread :rolleyes:

[QUOTE=xilman;606363]Substantially beyond the limits of the 2- Cunningham table.

Don't let that stop you from trying to find more factors though.[/QUOTE]For instance:
[code]
pcl@thoth:~/Astro/Misc$ ecm 10000
GMP-ECM 7.0.4 [configured with GMP 6.2.1, --enable-asm-redc] [ECM]
(2^7363-1)/223
Input number is (2^7363-1)/223 (2215 digits)
Using B1=10000, B2=1678960, polynomial x^1, sigma=0:17348063569600894463
Step 1 took 838ms
Step 2 took 724ms
********** Factor found in step 2: 4816405503271
Found prime factor of 13 digits: 4816405503271
Composite cofactor ((2^7363-1)/223)/4816405503271 has 2202 digits
((2^7363-1)/223)/4816405503271
Input number is ((2^7363-1)/223)/4816405503271 (2202 digits)
Using B1=10000, B2=1678960, polynomial x^1, sigma=0:17644336739200299761
Step 1 took 833ms
********** Factor found in step 1: 616318177
Found prime factor of 9 digits: 616318177
Composite cofactor (((2^7363-1)/223)/4816405503271)/616318177 has 2193 digits

[/code]That was, of course, rather silly. Because we know that 7363 = 37*199 there are some obvious algebraic factors. It was easier for me to type in ((2^7363-1)/223)/4816405503271 than to perform the algebra.

[QUOTE=xilman;606367]For instance:
[code]
pcl@thoth:~/Astro/Misc$ ecm 10000
GMP-ECM 7.0.4 [configured with GMP 6.2.1, --enable-asm-redc] [ECM]
(2^7363-1)/223
Input number is (2^7363-1)/223 (2215 digits)
Using B1=10000, B2=1678960, polynomial x^1, sigma=0:17348063569600894463
Step 1 took 838ms
Step 2 took 724ms
********** Factor found in step 2: 4816405503271
Found prime factor of 13 digits: 4816405503271
Composite cofactor ((2^7363-1)/223)/4816405503271 has 2202 digits
((2^7363-1)/223)/4816405503271
Input number is ((2^7363-1)/223)/4816405503271 (2202 digits)
Using B1=10000, B2=1678960, polynomial x^1, sigma=0:17644336739200299761
Step 1 took 833ms
********** Factor found in step 1: 616318177
Found prime factor of 9 digits: 616318177
Composite cofactor (((2^7363-1)/223)/4816405503271)/616318177 has 2193 digits

[/code]That was, of course, rather silly. Because we know that 7363 = 37*199 there are some obvious algebraic factors. It was easier for me to type in ((2^7363-1)/223)/4816405503271 than to perform the algebra.[/QUOTE]For an odd prime p, any prime factor q of 2^p - 1 is of the form 2*k*p+1, k integer; in particular, q > p.

This leads to a ludicrous proof of compositeness and factorization:

The fact that 223 divides 2^7363 - 1 though 223 < 7363 proves that 7363 is composite.

Factoring 223 - 1 or 222, we get the prime factors 2, 3, and 37. And 37 divides 7363, the quotient being 199.

Curiously, the factor 4816405503271 divides the "primitive part" (2^7363 - 1)/(2^37 - 1)/(2^199 - 1) of 2^7363 - 1. The cofactor (2^7363 - 1)/(2^37 - 1)/(2^199 - 1)/4816405503271 is composite.

[QUOTE=James Heinrich;606358]Record-size Mersenne factors are automatically reported to Paul Zimmerman (and Richard Brent for ECM) during the nightly data sync. The codepath for auto-reporting P-1 factors hasn't yet been tested (nobody has found a sufficiently large P-1 factor since I wrote the code in 2020) so tonight will be its test. Wouldn't hurt for [i]nordi[/i] to email him anyways.[/QUOTE]

I see that Paul's list still hasn't ben updated. Did the code work correctly?

[QUOTE=charybdis;606708]I see that Paul's list still hasn't ben updated. Did the code work correctly?[/QUOTE]It did, the email was sent, perhaps he's on vacation or something?

[QUOTE=James Heinrich;606709]It did, the email was sent, perhaps he's on vacation or something?[/QUOTE]

Well there's a factor from 27 May on his top-10 ECM page for this year. Maybe he needs a nudge.

[QUOTE=charybdis;606854]Well there's a factor from 27 May on his top-10 ECM page for this year. Maybe he needs a nudge.[/QUOTE]I talked to him earlier today, I imagine he will get the page updated sometime over the next few days.

[QUOTE=James Heinrich;606855]I talked to him earlier today, I imagine he will get the page updated sometime over the next few days.[/QUOTE]He replied:[quote=Paul Zimmerman]for some reason I missed that report. It is now #10 on the list.
[url]https://members.loria.fr/PZimmermann/records/Pminus1.html[/url][/quote]

P-1 found a factor in stage #1, B1=494000.
UID: Jwb52z/Clay, M115693873 has a factor: 1952359233750913828524289 (P-1, B1=494000)

80.691 bits.

I've been running large P-1 on 4.96M to 4.97M without much luck (3 factors in 84 attempts, P-1 calculator predicts 12% increase in factor probability), with a success this morning! M4963463 has factor 740152403849563084825547533175743, 109.190 bits.

I've wondered whether these dry streaks are just bad luck, or if there is something wrong with my machine. I ran some P-1 tests that had previously found factors and all factors were found again, so I would expect not (maybe something tends to go wrong in the longer runs but not in the shorter ones?) Does anyone have any suggestions/ideas for how better to test?

[QUOTE=Denial140;607349]I've wondered whether these dry streaks are just bad luck, or if there is something wrong with my machine.

Does anyone have any suggestions/ideas for how better to test?[/QUOTE]
The first question is valid, and the answer is - yes, both are possible.

Consider this analogy:
"I buy lottery tickets, fill in six numbers, and then scan them, and then wait to win. Sometimes I win twice in a row, and sometimes I have weeks and weeks without a win.
I've wondered whether these dry streaks are just bad luck, or if there is something wrong with my filling the tickets. Maybe my pen is broken, maybe I not filling the bubbles completely so that the lottery scanner cannot read them?"
Sure - both are possible.
Re: luck - Same as the poisson process of drawing a card from a deck and expect an ace. Sometimes you will draw two aces in a row, maybe even three, and sometimes you can draw 50 times and not get an ace.

For the second question - follow the analogy. Is there a better way to win in a lottery? Just like with the lottery, there are trivial solutions, for example with unlimited money buy _all_ the tickets, you will be guaranteed to win. Impractical though.

[QUOTE=Batalov;607362]For the second question - follow the analogy. Is there a better way to win in a lottery? Just like with the lottery, there are trivial solutions, for example with unlimited money buy _all_ the tickets, you will be guaranteed to win. Impractical though.[/QUOTE]

Sorry, I was not clear - I mean specifically testing for machine errors without taking too long.

Ah. Run the stability test (a.k.a. torture) - it is built in the program. Many folks run it once they have just built a new machine, for 24 - 48+ hours (best to run for several ambient temperature cycles - day/night. continuously). The key is - the code [I]knows [/I]the true answer so it can compare. *

It is hard to test otherwise (when answer is unknown).

____
* that actually reminded me to run that too, - summer is here. It is good to run the torture test at least once a year, too.

[QUOTE=Batalov;607362]
For the second question - follow the analogy. Is there a better way to win in a lottery? Just like with the lottery, there are trivial solutions, for example with unlimited money buy _all_ the tickets, you will be guaranteed to win. Impractical though.[/QUOTE]

The best way to win the lottery is not to buy any tickets. That way you don't lose, and since the opposite of a loss is a win ...

Two composite factors in a single day
 

I didn't think I was ever going to get a P-1 factor that I thought was worthy of posting here; but, today (PDT), I found [M]8879293[/M] has a composite factor, 1952505446389508559973390809501412786062062585404808923663962210457688947228452593 (270.042 bits):
[URL="https://www.mersenne.ca/factor/509948624278384111727110637486537527543"]509948624278384111727110637486537527543[/URL] (128.584 bits) and [URL="https://www.mersenne.ca/factor/3828827755251720703479206898096918957995351"]3828827755251720703479206898096918957995351[/URL] (141.458 bits)
Also found today, but slightly less impressive, I found [M]8859827[/M] has a composite factor, 35645538757884671884030612032344482636735761042071 (164.608 bits):
[URL="https://www.mersenne.ca/factor/39185475778814976961751"]39185475778814976961751[/URL] (75.053 bits) and [URL="https://www.mersenne.ca/factor/909662012504027897396320321"]909662012504027897396320321[/URL] (89.565 bits)
My first ever double composite in a single day.

[QUOTE=linament;608140]I didn't think I was ever going to get a P-1 factor that I thought was worthy of posting here; but, today (PDT), I found [M]8879293[/M] has a composite factor, 1952505446389508559973390809501412786062062585404808923663962210457688947228452593 (270.042 bits):
[URL="https://www.mersenne.ca/factor/509948624278384111727110637486537527543"]50994862427838411172711063748653752754[/URL] (128.584 bits) and [URL="https://www.mersenne.ca/factor/3828827755251720703479206898096918957995351"]3828827755251720703479206898096918957995351[/URL] (141.458 bits)
Also found today, but slightly less impressive, I found [M]8859827[/M] has a composite factor, 3564553875788467188403061203234448263673576104207 (164.608 bits):
[URL="https://www.mersenne.ca/factor/39185475778814976961751"]39185475778814976961751[/URL] (75.053 bits) and [URL="https://www.mersenne.ca/factor/909662012504027897396320321"]909662012504027897396320321[/URL] (89.565 bits)
My first ever double composite in a single day.[/QUOTE]

Your factors are completely wrong.

50994862427838411172711063748653752754[B]3[/B] instead of 50994862427838411172711063748653752754

3564553875788467188403061203234448263673576104207[B]1[/B] instead of 3564553875788467188403061203234448263673576104207

[QUOTE=linament;608140]I didn't think I was ever going to get a P-1 factor that I thought was worthy of posting here; but, today (PDT), I found [M]8879293[/M] has a composite factor, 1952505446389508559973390809501412786062062585404808923663962210457688947228452593 (270.042 bits):
[URL="https://www.mersenne.ca/factor/509948624278384111727110637486537527543"]50994862427838411172711063748653752754[/URL] (128.584 bits) and [URL="https://www.mersenne.ca/factor/3828827755251720703479206898096918957995351"]3828827755251720703479206898096918957995351[/URL] (141.458 bits)
Also found today, but slightly less impressive, I found [M]8859827[/M] has a composite factor, 3564553875788467188403061203234448263673576104207 (164.608 bits):
[URL="https://www.mersenne.ca/factor/39185475778814976961751"]39185475778814976961751[/URL] (75.053 bits) and [URL="https://www.mersenne.ca/factor/909662012504027897396320321"]909662012504027897396320321[/URL] (89.565 bits)
My first ever double composite in a single day.[/QUOTE]
:showoff::tu: - the larger factor is 43rd on the all time p-1 Mersenne factor list!

Find of the day: [URL="https://www.mersenne.ca/exponent/9491897"]9491897[/URL]

145.7 bits, personal record.

[QUOTE=tha;608161]Find of the day: [URL="https://www.mersenne.ca/exponent/9491897"]9491897[/URL] 145.7 bits, personal record.[/QUOTE]Impressive! :cool:

[QUOTE=tha;608161]Find of the day: [URL="https://www.mersenne.ca/exponent/9491897"]9491897[/URL]

145.7 bits, personal record.[/QUOTE]

And a 127.6 bits find within 24 hours thereafter: [URL="https://www.mersenne.ca/exponent/9493151"]9493151[/URL]

An absolute unit:

[QUOTE=masser;608242]An absolute unit:[/QUOTE][M]M27506879[/M] has a 230.239-bit (70-digit) [b]composite[/b] (P22+P23+P26) factor: [url=https://www.mersenne.ca/M27506879]2036174125816121071359980479118739320526578640539327308453173168258209[/url] (P-1,B1=285000,B2=34496700)
Exponent had 3 previously-known factors, now it has 3 more for a total of 6. :smile:

P-1 found a factor in stage #2, B1=495000, B2=14113000.
UID: Jwb52z/Clay, M115819853 has a factor: 389465490663842528068121 (P-1, B1=495000, B2=14113000)

78.366 bits.

P-1 found a factor in stage #2, B1=490000, B2=13984000.
UID: Jwb52z/Clay, M114758353 has a factor: 3328576113941665489451567 (P-1, B1=490000, B2=13984000)

81.461 bits.

P-1 found a factor in stage #1, B1=495000.
UID: Jwb52z/Clay, M115896083 has a factor: 57722400286012225410987976001 (P-1, B1=495000)

95.543 bits.

P-1 found a factor in stage #1, B1=495000.
UID: Jwb52z/Clay, M115932499 has a factor: 31496057732563307067135799 (P-1, B1=495000)\

84.703 bits.

[QUOTE=Jwb52z;608862]P-1 found a factor in stage #2, B1=490000, B2=13984000.
UID: Jwb52z/Clay, M114758353 has a factor: 3328576113941665489451567 (P-1, B1=490000, B2=13984000)

81.461 bits.[/QUOTE]

You'd better upgrade Prime95 to the latest version of 30.8 to enjoy the P-1 speedup.

P-1 found a factor in stage #2, B1=495000, B2=14132000.
UID: Jwb52z/Clay, M115980679 has a factor: 35021896406377410743734681239671 (P-1, B1=495000, B2=14132000)

104.788 bits.

[QUOTE=Jwb52z;610340]UID: Jwb52z/Clay, M[M]115980679[/M] has a factor[/QUOTE]Still on v30.7b9... see [url]https://www.mersenne.org/download/[/url] :smile:

[QUOTE=BudgieJane;607805]The best way to win the lottery is not to buy any tickets.[/QUOTE]The best way to win is to run the lottery and sell tickets.

Or, if there are oppressive laws in your area that forbid you doing that, then rig it in your favour, or bribe the programmer, or similar.

[QUOTE=retina;610368]The best way to win is to run the lottery and sell tickets.

Or, if there are oppressive laws in your area that forbid you doing that, then rig it in your favour, or bribe the programmer, or similar.[/QUOTE]This brings to mind a criminal case I'd heard about some years back.

<google google>

Found it. The following news story from January 2022 is about the case.

[url=https://iowacapitaldispatch.com/2022/01/27/lottery-scams-alleged-mastermind-is-paroled-after-4-1-2-years-in-prison/]Lottery scam's alleged mastermind is paroled after 4 1/2 years in prison[/url][quote]<snip>
The Iowa Board of Parole has approved the release of Eddie Tipton, the former information security director of the Multi-State Lottery Association based in Urbandale. Tipton was arrested in 2015 and accused of installing computer code on lottery computers that allowed him to predict the winning numbers.

His efforts to rig the drawings were uncovered after Iowa Lottery officials grew suspicious over an anonymous attempt to claim a $16.5 million Hot Lotto jackpot. They eventually linked Tipton, his brother, Tommy, and a longtime friend, Robert Rhodes, to suspicious winnings claimed in five states.
<snip>[/quote]

P-1 found a factor in stage #2, B1=1000000, B2=354388650 on a Mac OS X 64-bit,v30.8,build 15

UID: harlee/i5-5250U_1600, M[URL="https://www.mersenne.ca/exponent/7978781"]7978781[/URL] has a factor: 3972308628969248687924140052597030897 (P-1, B1=1000000, B2=354388650)

121.579 bits

P-1 found a factor in stage #2, B1=660000, B2=53460000

UID: harlee/i5-5250U_1600, M[URL="https://www.mersenne.ca/exponent/8051803"]8051803 [/URL]has a factor: 3659124125202063740433468127527432673 (P-1, B1=660000, B2=53460000),

121.461 bits

P-1 found a factor in stage #2, B1=488000, B2=12420000.
UID: Jwb52z/Clay, M116162087 has a factor: 63220472344899739179621176191 (P-1, B1=488000, B2=12420000)

95.674 bits.