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-   -   Found a factor, sunshine? Embalm and entomb it here! (RU "Выкрасить и выбросить")) (https://www.mersenneforum.org/showthread.php?t=13977)

Dubslow 2012-03-23 23:54

I've only ever had one factor break 90, and that was 90.3.

flashjh 2012-03-24 00:05

[QUOTE=Dubslow;293960]I've only ever had one factor break 90, and that was 90.3.[/QUOTE]
[URL="http://mersenne-aries.sili.net/exponent.php?exponentdetails=52038281"]M52038281[/URL] is my largest, so far, but it is small compared to the others reported on [URL="http://mersenne-aries.sili.net/stats.php?showuserstats=*"]James' site[/URL].

Dubslow 2012-03-24 00:30

Heh, it says I have the largest TF factor... I need to upload some results files, apparently...

[url]http://mersenne-aries.sili.net/exponent.php?factordetails=3907182061566328992465817[/url]


Edit: Re-uploaded that line; I remember now that's how I figured out his site didn't recognize the E when a factor was found, after 27.4 came out. (James, you might wanna delete that factor line... :smile:)

Edit2: Grrr, another [URL="http://mersenne-aries.sili.net/exponent.php?exponentdetails=49705543"]tiny one[/URL]...

flashjh 2012-03-24 03:41

[QUOTE=Dubslow;293968]Heh, it says I have the largest TF factor... I need to upload some results files, apparently...

[URL]http://mersenne-aries.sili.net/exponent.php?factordetails=3907182061566328992465817[/URL]


Edit: Re-uploaded that line; I remember now that's how I figured out his site didn't recognize the E when a factor was found, after 27.4 came out. (James, you might wanna delete that factor line... :smile:)

Edit2: Grrr, another [URL="http://mersenne-aries.sili.net/exponent.php?exponentdetails=49705543"]tiny one[/URL]...[/QUOTE]
Still 75.[SIZE=2]643 bits... way outside 'normal' TF and above G272 TF level for that exponent.[/SIZE]

Dubslow 2012-03-24 03:46

[QUOTE=flashjh;293988]Still 75.[SIZE=2]643 bits... way outside 'normal' TF and above G272 TF level for that exponent.[/SIZE][/QUOTE]

Small comfort :razz:


By the way, looking back through this thread, ckdo found a 15x size factor in the 3xx,xx range (I might have the power of ten wrong).

flashjh 2012-03-24 03:49

[QUOTE=Dubslow;293991]Small comfort :razz:


By the way, looking back through this thread, ckdo found a 15x size factor in the 3xx,xx range (I might have the power of ten wrong).[/QUOTE]
I remember one very large one, but it was composite... is that the one?

Dubslow 2012-03-24 04:14

[QUOTE=flashjh;293992]I remember one very large one, but it was composite... is that the one?[/QUOTE]

...Crap. That's what I get for skimming :P

Anyone know what the smallest not-fully-factored Mersenne-prime-exponent number is? (PrimeNet's database would be almost impossible to go through. James, can you implement a "Next" button on your site?)

bcp19 2012-03-24 04:43

[QUOTE=Dubslow;293993]...Crap. That's what I get for skimming :P

Anyone know what the smallest not-fully-factored Mersenne-prime-exponent number is? (PrimeNet's database would be almost impossible to go through. James, can you implement a "Next" button on your site?)[/QUOTE]

[URL="http://mersenne-aries.sili.net/exponent.php?exponentdetails=947"][COLOR=#000080]M947[/COLOR][/URL] is the smallest one that has at least 4 known factors so far, but I know M929 is not fully factored. There is likely smaller, but you'd probably need James to find it.

rcv 2012-03-24 06:18

[QUOTE=Dubslow;293993]Anyone know what the smallest not-fully-factored Mersenne-prime-exponent number is?[/QUOTE]
See the Cunningham Project's "First Five Holes":
[URL="http://homes.cerias.purdue.edu/%7Essw/cun/champ"]http://homes.cerias.purdue.edu/~ssw/cun/champ[/URL]

2^929-1 is the smallest Mersenne Number that's not completely factored. But probably not for too long. See the reservations page:
[URL="http://homes.cerias.purdue.edu/%7Essw/cun/who"]http://homes.cerias.purdue.edu/~ssw/cun/who[/URL]

Or click below if you want to see the current five "holes" in Sid's database
[URL="http://www.factordb.com/index.php?query=2%5Ek-1&use=k&k=929&VP=on&EV=on&OD=on&CF=on&C=on&perpage=5&format=1&sent=Show"]http://www.factordb.com/...[/URL]

Dubslow 2012-03-24 06:59

What's the smallest one that isn't reserved by some other project?

drh 2012-03-24 11:57

[QUOTE=flashjh;293965][URL="http://mersenne-aries.sili.net/exponent.php?exponentdetails=52038281"]M52038281[/URL] is my largest, so far, but it is small compared to the others reported on [URL="http://mersenne-aries.sili.net/stats.php?showuserstats=*"]James' site[/URL].[/QUOTE]

Just curious why James' site doesn't have my factor of M56226553 listed under the Top 10. Looks like it would be #3, at 126+ bits. (see post #196 in this thread)

flashjh 2012-03-24 12:16

[QUOTE=drh;294021]Just curious why James' site doesn't have my factor of M56226553 listed under the Top 10. Looks like it would be #3, at 126+ bits. (see post #196 in this thread)[/QUOTE]
Did you upload your results file to his site?

wreck 2012-03-25 09:34

[Sun Mar 25 10:56:00 2012]
P-1 found a factor in stage #2, B1=535000, B2=5751250.
UID: wreck2002/wreck_wyl, M55970573 has a factor: 1772243243359193295946580551, AID: 88E5D86EC28A7E487811BAF66AA785F7

k = 3 * 5^2 * 643 * 743 * 193463 * 2283887
This is my first P-1 factor.

Dubslow 2012-03-30 19:44

Herk, remarkably low size for remarkably high B2 saturation
[url]http://mersenne-aries.sili.net/exponent.php?factordetails=15536852122405273877641[/url]

k=2^2 × 3 × 5 × 282,239 × 9,234,991
73.7 bits
B2=9,700,000,
B2 saturation = 9,234,991/9,700,000 = 95.21%

TObject 2012-03-31 02:05

M56355547 has a factor: 5109242810232110450137
k = 2^2 * 3 * 211 * 17903015017 = 45330434023044

M67604689 has a factor: 793400402485575837791
k = 5 * 61 * 3259 * 5903389 = 5867939149055

M67604389 has a factor: 676273206848992081873
k = 2^3 * 3 * 41 * 283 * 811 * 22147 = 5001696020424

M369111439 has a factor: 248870925861776838239
k = 337121665121 is prime

M369111331 has a factor: 2395448792646190676561
k = 2^3 * 5 * 11^2 * 227 * 761 * 3881 = 3244886557880

c10ck3r 2012-04-03 20:23

M91200101 has a factor: 2[COLOR=#990000]^2[/COLOR] × 3 × 11 × 41 × 127 × 429409 x p
M91200713 has a factor: 3 × 11 × 12074873471 x p
M91200743 has a factor: 23^2 × 926869513 x p
M91201171 has a factor: 2[COLOR=#990000]^2[/COLOR] × 5 × 21569 × 1335239 x p
M91204657 has a factor: 2[COLOR=#990000]^3[/COLOR] × 3 × 5 × 11 × 383 × 577 × 761 x p
M91206281 has a factor: 3[COLOR=#990000]^2[/COLOR] × 7 × 11 × 373 × 1304227 x p
M91207357 has a factor: 369391100747 x p
M91210027 has a factor: 2[COLOR=#990000]^4[/COLOR] × 13 × 41 × 1093 × 25117 x p
M91210813 has a factor: 3[COLOR=#990000]^2[/COLOR] × 17 × 787 × 2085841 x P
M91211117 has a factor: 2[COLOR=#990000]^5[/COLOR] × 5[COLOR=#990000]^2[/COLOR] × 19[COLOR=#990000]^2[/COLOR] × 61 × 20399 x P
M91211513 has a factor: 3469 × 4651 × 20353 x p


I'll spare you the other ~890 for larger exponets :)

Batalov 2012-04-04 02:48

The factors are two times more plus 1, really.

flashjh 2012-04-04 03:14

Found a nice 'k' today:

[URL="http://mersenne-aries.sili.net/exponent.php?exponentdetails=79943021"]M79943021[/URL]
Factor = 2217770314776436337081
k = 2^[SIZE=2]2 * 5 * 227 * [COLOR=red]3055273981[/COLOR][/SIZE]
Digits = 22
Bits = 70.910

Another interesting k

[URL="http://mersenne-aries.sili.net/exponent.php?exponentdetails=79943693"]M79943693[/URL]
Factor = 6794411101274465993903
k = 43 × 1009 × 979440361
Digits = 22
Bits = 72.525

Dubslow 2012-04-04 04:37

Are those P-1 or TF?

cheesehead 2012-04-04 05:13

With k factors near 3 billion and 1 billion -- my guess would be TF

Dubslow 2012-04-04 05:20

[QUOTE=cheesehead;295351]With k factors near 3 billion and 1 billion -- my guess would be TF[/QUOTE]

I've had a k factor up at 346M with the B-S extension, and as we know Mr. Hallet has a [i]ton[/i] of memory. So I just wanted to be sure, though I agree TF is more likely. (Also those expos are outside of his P-1 work size, if [URL="http://gpu72.com/reports/worker/b49e80e9382626afc7ebe2f81662dadb/"]this[/URL] or [URL="http://gpu72.com/reports/workers/p-1/graph/1-10/"]this[/URL] are anything to go by. :smile:)

cheesehead 2012-04-04 05:27

I'm willing to be amazed by being wrong. :-)

flashjh 2012-04-04 07:35

[QUOTE=Dubslow;295347]Are those P-1 or TF?[/QUOTE]

Yes, they're both TF. I wish they were P-1 since I still haven't seen a B-S factor.

Batalov 2012-04-04 22:00

Got my 100th factor for GPU72.
Now I need to overtake Greg before he employs the same strategem (which is too easy)

harlee 2012-04-05 13:04

P-1 found a factor in stage #2, B1=135000, B2=2733750, E=6.
M4421467 has a factor: 8546596152478901798249 (73 bits)

k=2^2 × 11 × 541 × 3,301 × 12,299,893

Dubslow 2012-04-05 19:36

I believe that's the first E=6 B-S factor I've seen. Nice going!

flashjh 2012-04-06 02:06

Found a nice stage-1 factor: 405845656468221226445605471

[URL="http://mersenne-aries.sili.net/exponent.php?exponentdetails=50647693"]M50647693[/URL]
bits: 88.391
digits: 27
k = 3 × 5 × 907 × 17959 × 55229 × 296909

Stef42 2012-04-07 11:22

Found some factors while running some 50 random exponents at 98M from 65 to 67.

found 1 factor for M98071543 from 2^65 to 2^67 [mfaktc 0.18 barrett79_mul32]
M98071543 has a factor: 146536851648186392249 [TF:65:67:mfaktc 0.18 barrett79_mul32]

k = 2[SUP]2[/SUP] × 83 × [COLOR="Red"]2250275899[/COLOR]


M98073133 has a factor: 55134581081542102081 [TF:65:67:mfaktc 0.18 barrett79_mul32]
found 1 factor for M98073133 from 2^65 to 2^67 [mfaktc 0.18 barrett79_mul32]

k = 2[SUP]5[/SUP] × 3[SUP]2[/SUP] × 5 × 757 × 257861

M98071789 has a factor: 101395775139293311447 [TF:65:67:mfaktc 0.18 barrett79_mul32]
found 1 factor for M98071789 from 2^65 to 2^67 [mfaktc 0.18 barrett79_mul32]

k = 3 × 7 × 11[SUP]2[/SUP] × 203442227

M98174059 has a factor: 126812702311349093167 [TF:65:67:mfaktc 0.18 barrett79_mul32]
found 1 factor for M98174059 from 2^65 to 2^67 [mfaktc 0.18 barrett79_mul32]

k = 3 × 10949 × 19662571

Dubslow 2012-04-10 03:26

Found a P-1 factor in the standard LL range with k not having a factor of 2.
[url]http://www.mersenne-aries.sili.net/exponent.php?exponentdetails=52996729[/url]

3 × 5 × 53 × 4397 × 18911 × 61231
78.* bits.

Batalov 2012-04-10 06:40

[QUOTE=Dubslow;295980]with k not having a factor of 2.[/QUOTE]
Wow! What are the chances of that? [SPOILER]... 50% ?[/SPOILER]

Dubslow 2012-04-10 07:24

It's the first one I can recall, out of 25.

axn 2012-04-10 13:47

[QUOTE=Batalov;296001]Wow! What are the chances of that? [SPOILER]... 50% ?[/SPOILER][/QUOTE]

Across all factors, it should be 50%. But across P-1 factors, it should be much less. Why? :smile:

Batalov 2012-04-10 18:41

In Stage 1 factors, should be 100%! [SPOILER]Proof: I have only one of these in results.txt and it has an odd k: M52361579 has a factor: 3833960913376723923372391[/SPOILER] :missingteeth:

LaurV 2012-04-11 03:16

[QUOTE=Dubslow;295980]Found a P-1 factor in the standard LL range with k not having a factor of 2.
[URL]http://www.mersenne-aries.sili.net/exponent.php?exponentdetails=52996729[/URL]

3 × 5 × 53 × 4397 × 18911 × 61231
78.* bits.[/QUOTE]

[QUOTE=Batalov;296001]Wow! What are the chances of that? [SPOILER]... 50% ?[/SPOILER][/QUOTE]

[QUOTE=axn;296028]Across all factors, it should be 50%. But across P-1 factors, it should be much less. Why? :smile:[/QUOTE]

[QUOTE=Batalov;296044]In Stage 1 factors, should be 100%! [SPOILER]Proof: I have only one of these in results.txt and it has an odd k: M52361579 has a factor: 3833960913376723923372391[/SPOILER] :missingteeth:[/QUOTE]

The chance of k being odd is higher then 50%. Factors fall in two categories:
(1) of the form f=2kp+1 and f=8x+1
(2) of the form d=2kp+1 and d=8x-1

By solving each pair of conditions, factors of the form (1) are always 2kp+1=8x+1, so k is a multiple of 4 and we have in fact only factors of the form [B]8zp+1[/B]. These are the only factors with "even k" in the "classical" sense, not only even, but "quadruple k" too. There is no factor where k is equal to 2 (mod 4).

Same as above, factors of the form (2) will always be (by re-notation of k) of the form [B]8zp+sp+1[/B], where s=8-(p (mod 4)). So s=6 if p=4q+1, but s=2 if p=4q+3 for some q. We can factor a two out of it and we get the "k in the classical sense" is always odd, and the form 4z+t, where t=-p (mod 4).

So we have:
(1) factors of the form [B]f=2*[4*z]*p+1[/B].
(2) factors of the form [B]d=2*[4*z+t]*p+1[/B], t=-p (mod 4).
where the brackets were used to show the decomposition of k.

So, the "d-factors" always exists, for any composite Mp=2^p-1, for an odd prime p, because in this case Mp is 7 (mod 8), and it can't have only factors of the form f, because f is 1 (mod 8) and their set is close to multiplication (their product is always 1 (mod 8)). The conclusion is that a composite Mp may have any number of f-factors, but it MUST have an ODD number of d-factors, as the product of an even number of d-factors is also 1 (mod 8).

This shows that all composite Mp will have a factor with odd k, but some composites may exists which have no f-factors (they can be a product of 3, 5, 7, etc d-factors). There are more d-factors (odd k) then f-factors (quadruple k). There is no factor where k is 2 (mod 4).

axn 2012-04-11 03:32

This ...
[QUOTE=LaurV;296082]The chance of k being odd is higher then 50%. [/quote]
Does not follow from this ...
[QUOTE=LaurV;296082]So, the "d-factors" always exists, for any composite Mp=2^p-1, for an odd prime p, because in this case Mp is 7 (mod 8), and it can't have only factors of the form f, because f is 1 (mod 8) and their set is close to multiplication (their product is always 1 (mod 8)). The conclusion is that a composite Mp may have any number of f-factors, but it MUST have an ODD number of d-factors, as the product of an even number of d-factors is also 1 (mod 8).

This shows that all composite Mp will have a factor with odd k, but some composites may exists which have no f-factors (they can be a product of 3, 5, 7, etc d-factors). There are more d-factors (odd k) then f-factors (quadruple k). There is no factor where k is 2 (mod 4).[/QUOTE]

TObject 2012-04-11 19:04

M343111009 has a factor: 101147794026026459897
k = 2^2 * 103 * 357762281 = 147398059772

Stef42 2012-04-12 06:18

M36118457 has a factor: 204726728570332673759 [TF:67:68:mfaktc 0.18 barrett79_mul32]
found 1 factor for M36118457 from 2^67 to 2^68 [mfaktc 0.18 barrett79_mul32]

k = [COLOR="Red"]2834101254247[/COLOR] (21 digits)

Batalov 2012-04-17 23:02

Just noticed this in the "Recent cleared"
[CODE]Member Name Computer Name Exponent Type UTC Time Received Days GHz-days Result
-------------------- ---------------- --------- -------- ------------------- ----- -------- -------------------------------------------------
PPed72 Unimib 56261729 F-PM1 Apr 17 2012 9:20PM 10.9 4.0290 1531076005907436082137874576376865534182896705073
[/CODE]
(160.06 bits... Composite of course: = p24*p25)

TObject 2012-04-18 17:42

M55255747 has a factor: 2214689268597166059044783
k = 59 * 101 * 257 * 12323 * 1061897 = 20040352260527453

A tiny Intel Atom CPU powered computer found it on its first PM1 assignemnt.

alpertron 2012-04-20 14:17

Today my computer found a 132-bit prime:

[Fri Apr 20 08:12:57 2012]
P-1 found a factor in stage #1, B1=10000000.
M798257 has a factor: 4593821825255405094261984523461159901759
k = 3 × 83 × 149 × 1163 × 1223 × 16561 × 794033 × 1425649 × 2908519

I'm running B1 = 10M, B2 = 200M for all numbers in the range 790K to 800K and this is the 7th prime found so far.

Brain 2012-04-20 16:07

New P-1 all time high in this thread
 
[QUOTE=Brain;284711]How could I miss that... Sorry. Beat this![/QUOTE]

[QUOTE=alpertron;296925]Today my computer found a 132-bit prime:

[Fri Apr 20 08:12:57 2012]
P-1 found a factor in stage #1, B1=10000000.
M798257 has a factor: 4593821825255405094261984523461159901759
k = 3 × 83 × 149 × 1163 × 1223 × 16561 × 794033 × 1425649 × 2908519

I'm running B1 = 10M, B2 = 200M for all numbers in the range 790K to 800K and this is the 7th prime found so far.[/QUOTE]

It is prime. So, we have a new thread local record... Congrats!

c10ck3r 2012-04-23 23:43

[FONT=&quot]Found a notable one starting out my 84M run...
M84004787 has a factor: [B]12824399621243547529430624238490771516609 [/B]
k=2 ^ 5 x 3 x 313 x 4657 x [B]545482978807033815692147
[/B]Factors were-[/FONT][FONT=&quot][B]130229148576592177313 [/B]and [/FONT][FONT=&quot][B]98475646669079490593[/B], both found while taking to 67 bits. [B]XD[/B]
[/FONT]

ckdo 2012-04-24 06:40

[QUOTE=c10ck3r;297146][FONT=&quot]Found a notable one starting out my 84M run...
M84004787 has a factor: [B]12824399621243547529430624238490771516609 [/B]
k=2 ^ 5 x 3 x 313 x 4657 x [B]545482978807033815692147
[/B]Factors were-[/FONT][FONT=&quot][B]130229148576592177313 [/B]and [/FONT][FONT=&quot][B]98475646669079490593[/B], both found while taking to 67 bits. [B]XD[/B]
[/FONT][/QUOTE]

The notable part is that your misunderstanding of the "k" concept. :devil:

cheesehead 2012-04-24 07:21

[QUOTE=c10ck3r;297146][FONT=&quot]Found a notable one starting out my 84M run...
M84004787 has a factor: [B]12824399621243547529430624238490771516609 [/B]
< snip >
Factors were-[/FONT][FONT=&quot][B]130229148576592177313[/B][/FONT][/QUOTE][FONT=&quot]k = [/FONT] 2[sup]4[/sup] [COLOR=green]×[/COLOR] 48445583143[FONT=&quot]

[/FONT][QUOTE]and [FONT=&quot][B]98475646669079490593[/B][/FONT][/QUOTE][FONT=&quot]k = [/FONT] 2[sup]4[/sup] [COLOR=green]×[/COLOR] 36633197563

[QUOTE=ckdo;297175]The notable part is that your misunderstanding of the "k" concept. :devil:[/QUOTE]

But [FONT=&quot][B]12824399621243547529430624238490771516609[/B][/FONT] = 2 [COLOR=green]×[/COLOR] (2[sup]5[/sup][COLOR=green]×[/COLOR]3[COLOR=green]×[/COLOR]313[COLOR=green]×[/COLOR]4657[COLOR=green]×[/COLOR][URL="http://wims.unice.fr/wims/wims.cgi?session=NK0946EC05.16&cmd=reply&calc=check&check=545482978807033815692147"]545482978807033815692147[/URL]) [COLOR=green]×[/COLOR] 84004787 + 1, so that k does have meaning, too. Even though composite, this factor is of the form 2kp + 1.

(Now, that last k should not be compared to either of the preceding k's on some equal basis, because it's algebraically derivable from them, as Dubslow shows below.)

Dubslow 2012-04-24 07:31

[tex](2kp+1)*(2mp+1) = 4(km)(p^2)+2p(m+k)+1 = 2(2kmp+m+k)p+1 = 2(m[2kp+1]+k)p+1 = 2(k[2mp+1]+m)p+1[/tex]
[/sm88]

LaurV 2012-04-24 07:40

The guy made a joke (he is the joker, remember? see his id is "ciocker") and you all jumped to [strike]kill[/strike] adnotate (@cheesehead: :razz:) him, first of you saying nonsense, the second of you forgetting duplicated phrases in the text, and the third [B]losing a "p" on the way[/B] in that calculus, hehe, THAT is really funny :razz: :smile:

And by the way, you don't need to close the \tex box to write subscripts and superscripts...[TEX]x_1^2+x^3_4=x^{2^3}_{1_4}[/TEX]

cheesehead 2012-04-24 07:45

[QUOTE=LaurV;297179]The guy made a joke (he is the joker, remember? see his id is "ciocker") and you all jumped to kill him,[/QUOTE]"kill" ???

How about "annotate" ?

LaurV 2012-04-24 07:55

Now it looks much better, last 3 posts could be deleted (my two including this one, and cheesehead's one in between). Well, we lose the fun, but the thread would be clearer. Or well... the thread would be clearer, but we will lose the fun...

Dubslow 2012-04-24 08:04

[QUOTE=LaurV;297183]Now it looks much better, last 3 posts could be deleted (my two including this one, and cheesehead's one in between). Well, we lose the fun, but the thread would be clearer. Or well... the thread would be clearer, but we will lose the fun...[/QUOTE]

Since when was clarity ever our first goal? :razz::smile:
(Shows how little Tex I know :P)

Batalov 2012-04-24 08:16

(easy warm-up) M1091 has a prime factor 2·k·1091+1, where
[CODE]k = 179 · 69737 · 4086974693 · 7727500822367 · 10227820166017 · 196164761709907 · 8326159283085775335016522402181511923674994349944795840347158060798548700472189268029761648871175757465278359531733261197555258091948229635309347779196749685783
[/CODE]

M10169 has a prime factor 2·k·10169+1, where
[CODE]k = 2^4 · 3^3 · 11 · 18196183 · 967157656641434911 · 8437886386...17[SUB]<2988>[/SUB][/CODE]
:popcorn:

aketilander 2012-04-24 09:53

[QUOTE=Batalov;297187](easy warm-up) M1091 has a prime factor 2·k·1091+1

M10169 has a prime factor 2·k·10169+1[/QUOTE]

Question: Is it the largest factors of M1091 and M10169 which you have proved being prime?

firejuggler 2012-04-24 17:41

for M1091, yup this is the largest factor and for 10169 has only 2 factor, a P41 and a PRP3022

ET_ 2012-04-24 18:19

[QUOTE=firejuggler;297219]for M1091, yup this is the largest factor and for 10169 has only 2 factor, a P41 and a PRP3022[/QUOTE]

Anybody started a certification with primo on it?

Luigi

Batalov 2012-04-24 18:25

M10169: I've factored k yesterday (arguably not hard, and probably had been done before, but it wasn't in the FactorDB anyway) and left a certification on an old primo3.0.9. It is really slow.
For the fun of it, I've started a 4-thread certification with primo4.0a14 and it will probably take only a couple hours. I'll d/l it.

(EDIT: DB is going to immediately certify the cofactor obviously, as soon as prp2988 cert is d/l-ed.)

(EDIT2: M10169 FF wasn't new - search the forum; I took a few fully factored Mp with p>10,000 and ran a few curves on their k values for the largest factor - just to instigate a :popcorn: conversation)

markr 2012-04-26 12:38

Close to B2!
 
P-1 found a factor in stage #2, B1=505000, B2=9595000.
M52182167 has a factor: 2029482487582610831696273
k = 2^3 x 1049 x 242677 x 9548587
9548587 / 9595000 = 0.9952...

alpertron 2012-04-30 01:27

I found another large prime factor of a Mersenne number. Its length is 130 bits.

P-1 found a factor in stage #1, B1=10000000.
M799417 has a factor: 737227711675437329857373483171104386487

k = 3[SUP]2[/SUP] × 61 × 619 × 14207 × 202387 × 580687 × 791663 × 1026521

TObject 2012-04-30 18:47

M344111197 has a factor: 462638685260988598273
k = 2^10 * 3 * 218822479 = 672222655488

c10ck3r 2012-05-01 21:31

Anybody interested in my list of 1041 factors found thus far? I can sort for certain ranges of exponents if needed... shoot me a PM with your email and which ranges you are interested in. Thanks!

Stef42 2012-05-03 09:25

M746199263 has a factor: 91476779052406004953 [TF:65:66:mfaktc 0.18 barrett79_mul32]
M746199263 has a factor: 88811032749292964359 [TF:65:66:mfaktc 0.18 barrett79_mul32]
found 2 factors for M746199263 from 2^65 to 2^66 [mfaktc 0.18 barrett79_mul32]

Stats [URL="http://mersenne-aries.sili.net/exponent.php?exponentdetails=746199263"]link[/URL].

k = 3[SUP]4[/SUP] × 734678093

k = 2[SUP]2[/SUP] × 3 × 191 × 26743081

flashjh 2012-05-05 19:09

Found a nice K:

[URL="http://mersenne-aries.sili.net/exponent.php?exponentdetails=58453471"]M58453471[/URL]
Factor: 3893338465413479482783
Digits: 22
Bits: 71.722
[B]K = 3 × 11100961724507[/B]

markr 2012-05-06 20:59

Smooth
 
M54676967 has a factor: 420411039467695302913223737
89 bits, but so smooth*
2^2 × 3 × 7 × 167 × 293 × 569 × 593 × 1327 × 2089

[SIZE="1"][COLOR="Silver"]* I'd cue davieddy but he might choose Mancini over Santana.[/COLOR][/SIZE]

Dubslow 2012-05-07 01:53

[QUOTE=markr;298623]M54676967 has a factor: 420411039467695302913223737
89 bits, but so smooth*
2^2 × 3 × 7 × 167 × 293 × 569 × 593 × 1327 × 2089

[SIZE="1"][COLOR="Silver"]* I'd cue davieddy but he might choose Mancini over Santana.[/COLOR][/SIZE][/QUOTE]

Wow! Indeed, that is ridiculously awesome.

Here's the complete opposite: A [URL="http://mersenne-aries.sili.net/exponent.php?exponentdetails=56028041"]factor[/URL] so bumpy it's only by fluke that P-1 found it and not TF.

M56,028,041, k = 2^3 × 247309 × 13133213

lorgix 2012-05-08 11:52

I just found my first GPU-factor:

[CODE]M976212067 has a factor: 513655278767372311447 [TF:65:70:mfaktc 0.18 barrett79_mul32]
found 1 factor for M976212067 from 2^65 to 2^70 [mfaktc 0.18 barrett79_mul32][/CODE]

LaurV 2012-05-09 07:46

Welcome to the club! We wish you thousands of factors! :razz:
Be careful, is addictive!

c10ck3r 2012-05-10 18:02

[SIZE=2]554808873006599188633 is a factor of M[/SIZE][SIZE=2]31954267!
K= 2^2 x 3 x 760367 x 951437
My first DCTF factor found :)
[/SIZE]

TheJudger 2012-05-13 12:33

New personal record (9.83 "bits" bigger than my previous record): P-1 found a factor in stage #2, B1=515000, B2=10042500.
M55501499 has a factor: 4185864995365978016690272528312914075119 (131.62 Bits; k = 37709476958144662153091329373941 = 149 * 8623 * 17807 * 79579 * 145807 * 147139 * 965407)

Oliver

chalsall 2012-05-13 14:35

[QUOTE=TheJudger;299338]New personal record (9.83 "bits" bigger than my previous record): P-1 found a factor in stage #2, B1=515000, B2=10042500.
M55501499 has a factor: 4185864995365978016690272528312914075119 (131.62 Bits; k = 37709476958144662153091329373941 = 149 * 8623 * 17807 * 79579 * 145807 * 147139 * 965407)[/QUOTE]

Nice!!! A new record for [URL="http://www.gpu72.com/reports/largest_factors/"]GPU 72[/URL] too.

c10ck3r 2012-05-16 00:41

504927967098232939441 is a factor of M[SIZE=2]6,687,383.
Found as part of the rerun of poorly factored exponents.
k=2^3x3x5x37x56,543x150,377
[/SIZE]

TheJudger 2012-05-20 15:23

Only a few days after my new personal "factor size record" for P-1 factoring I've a new number two in my list:
P-1 found a factor in stage #2, B1=545000, B2=11581250.
M54945109 has a factor: 248355809127166139921362845673542274151 (127.54 Bits; k = 2260035639634149601208024227175 = 5 * 5 * 31 * 89 * 107 * 353 * 9437 * 60013 * 446951 * 3427093)

lorgix 2012-05-21 11:39

A few cases of Brent-Suyama paying off:

[CODE]P-1 found a factor in stage #2, B1=80000, B2=[COLOR=Red][B]1500000[/B][/COLOR].
UID: lorgix, M2139539 has a factor: 50417810253342889667777
k= 2^5*719*46747*[COLOR=Red][B]10954717[/B][/COLOR]

P-1 found a factor in stage #2, B1=85000, B2=[B][COLOR=Red]1742500[/COLOR][/B].
UID: lorgix, M2294807 has a factor: 4743377217925125644071
k= 3^3*5*751*3851*[B][COLOR=Red]2647063[/COLOR][/B]

P-1 found a factor in stage #2, B1=95000, B2=[COLOR=Red][B]1947500[/B][/COLOR].
UID: lorgix, M2442719 has a factor: 27573814760148300857
k= 2^2*37*907*[COLOR=Red][B]42045967[/B][/COLOR]

P-1 found a factor in stage #2, B1=95000, B2=[B][COLOR=Red]1947500[/COLOR][/B].
UID: lorgix, M2477309 has a factor: 412991649168730738883201
k= 2^6*5^2*1723*8167*[B][COLOR=Red]3702229[/COLOR][/B]

P-1 found a factor in stage #2, B1=95000, B2=[B][COLOR=Red]1947500[/COLOR][/B].
UID: lorgix, M2492143 has a factor: 189868506369595443867609863
k= 109*269*8663*74831*[COLOR=Red][B]2004109[/B][/COLOR]

P-1 found a factor in stage #2, B1=95000, B2=[B][COLOR=Red]1971250[/COLOR][/B].
UID: lorgix, M2492389 has a factor: 65384728464585460900369
k= 2^3*3*7*1847*4703*[COLOR=Red][B]8988337[/B][/COLOR]

P-1 found a factor in stage #2, B1=95000, B2=[B][COLOR=Red]1923750[/COLOR][/B].
UID: lorgix, M2433979 has a factor: 103825801661835930049
k= 2^5*3^2*47*193*[B][COLOR=Red]8164147[/COLOR][/B]

P-1 found a factor in stage #2, B1=160000, B2=[B][COLOR=Red]3680000[/COLOR][/B].
UID: lorgix, M8186687 has a factor: 1321002082390776639208561
k= 2^3*3^2*5*2687*14771*[COLOR=Red][B]5646577[/B][/COLOR][/CODE]And then a case of highly saturated B2:

P-1 found a factor in stage #2, B1=95000, B2=1947500.
UID: lorgix, M2444359 has a factor: 1588994437060952149274017
k= 2^4*3*31*41*197*13901*1945487

[B][COLOR=Red]1945487/1947500 ~= 0.999[/COLOR][/B]

KingKurly 2012-05-21 15:01

[Mon May 21 06:54:00 2012]
P-1 found a factor in stage #2, B1=285000, B2=[B]6341250[/B], E=6.
M43787581 has a factor: 4003395812858544808108690252822256209

---

M43787581 has factor 4003395812858544808108690252822256209 (121.59 bits)
k = 2^3 * 3^2 * 41 * 47 * 67 * 14083 * 22159 * 165601 * [B]95159089[/B]

:max:

Caught this during my sweep of doing P-1 on curtisc exponents that didn't get any in their first time around. I usually set tests saved to 1.1 and let slower machine pick them off. It only saves the double-check (assuming the first check was valid) but the bounds are adjusted downward, as appropriate... sometimes, you get lucky and find a factor anyway.

Bdot 2012-05-25 12:01

late game success
 
This one was almost finished ...
Sure, each class has the same chances, but so far I had not noticed a success in the almost-final round.

[code]
got assignment: exp=57347131 bit_min=71 bit_max=72
Starting trial factoring M57347131 from 2^71 to 2^72 (8.34GHz-days)
k_min = 20586759963000 - k_max = 41173519934847
Using GPU kernel "barrett15_75"
No checkpoint file "M57347131.ckp" found.
[date time] exp[TF bits]: percent class #, seq GHz time | ETA | #FCs | rate |SieveP. | CPU idle
[May 25 02:14] M57347131[71-72]: 99.17% 4581/4620,952/960 48.96 15.330s | 2m03s | 855.64M | 55.81M/s | 101050 | 0us = 0.00%
Result[00]: M57347131 has a factor: 2858577001937559485743

found 1 factor for M57347131 from 2^71 to 2^72 (partially tested) [mfakto 0.11 barrett15_75_4]
tf(): total time spent: 3h 59m 32.548s
[/code]

PageFault 2012-06-01 01:03

[CODE]P-1 found a factor in stage #2, B1=810000, B2=21060000.
UID: PageFault/boxen_01, M70002167 has a factor: 23343692938910511396401,[/CODE]

k is pretty rough:

2^3 * 5^2 * 714223 * 1167251

PageFault 2012-06-01 01:22

[CODE]P-1 found a factor in stage #1, B1=95000.
UID: PageFault/boxen_01, M8360353 has a factor: 123253905513130626056631481[/CODE]

This one should have been found in the original run.

k:

2^2 * 3^2 * 5 * 7 * 41 * 431 * 1289 * 4073 * 63059

flashjh 2012-06-04 18:50

[CODE][Mon Jun 04 09:47:31 2012]
P-1 found a factor in stage #1, B1=545000.
UID: flashjh/TF3, [URL="http://mersenne-aries.sili.net/exponent.php?exponentdetails=54885641"]M54885641[/URL] has a factor: 10917788677651143296532439[/CODE]

10917788677651143296532439 is [URL="http://mersenne-aries.sili.net/factor.php?n=10917788677651143296532439"]Prime[/URL]

c10ck3r 2012-06-04 20:32

[SIZE=2]45999635683923857777
[/SIZE][SIZE=2]263130442175552567999
are both factors of 2^340012417-1. Found running 65-68 bits, continuing on up.
[/SIZE]

c10ck3r 2012-06-04 22:40

Quick Q?
 
[QUOTE=c10ck3r;301253][SIZE=2]45999635683923857777
[/SIZE][SIZE=2]263130442175552567999
are both factors of 2^340012417-1. Found running 65-68 bits, continuing on up.
[/SIZE][/QUOTE]

Anyone else obsessed/as fanatical as me about finding multiple factors for numbers outside of the LL/DC wavefront?

Dubslow 2012-06-04 23:42

[QUOTE=c10ck3r;301270]Anyone else obsessed/as fanatical as me about finding multiple factors for numbers outside of the LL/DC wavefront?[/QUOTE]

Personally, no. I'm just waiting until quantum computers get under way, with their polynomial-factoring-algorithms. The current record holder is 143=11*13.

Brain 2012-06-05 05:32

[QUOTE=c10ck3r;301270]Anyone else obsessed/as fanatical as me about finding multiple factors for numbers outside of the LL/DC wavefront?[/QUOTE]
:smile: I am not alone... But I'm satisfied to find the first known factor. Currently upping 2M to 2^62.

PageFault 2012-06-07 01:48

You are not alone ... I'm getting all sort of crazy ideas for P-1. Can't act out on this at the moment - current machine is crap. When I do replace it, I will be going for a minimum of 64 GB of ram (even that is too low). All depends on the next job I find ... that is not too far off and I found that I am worth far more than I imagined, and my sector is booming ...

[QUOTE=c10ck3r;301270]Anyone else obsessed/as fanatical as me about finding multiple factors for numbers outside of the LL/DC wavefront?[/QUOTE]

flashjh 2012-06-09 20:49

[CODE]
got assignment: exp=57606359 bit_min=71 bit_max=72
Starting trial factoring M57606359 from 2^71 to 2^72
k_min = 20494119764580
k_max = 40988239535062
Using GPU kernel "barrett79_mul32"
class | candidates | time | ETA | avg. rate | SievePrimes | CPU wait
429/4620 | 1.03G | 10.415s | 2h31m | 98.87M/s | 10816 | 3.62%
M57606359 has a factor: 3086670355345499795863
found 1 factor for M57606359 from 2^71 to 2^72 (partially tested) [mfaktc 0.18 barrett79_mul32]
[B]tf(): total time spent: 15m 40.284s[/B]

[/CODE]
Always nice to find a factor fast

PageFault 2012-06-10 01:54

Right on mate. I remember back in the day, we often found 58 or 59 bit factors within minutes. I once did this with a pentium 133 ... three minutes into the run, which took close to a month if no factor was found.

Let's see ... M15xxxxxx, 58 to 65 bits, these days might take half an hour ... no idea, but maybe a good gpu in minutes ...

flashjh 2012-06-10 21:48

[QUOTE=PageFault;301900]Right on mate. I remember back in the day, we often found 58 or 59 bit factors within minutes. I once did this with a pentium 133 ... three minutes into the run, which took close to a month if no factor was found.[/QUOTE]
Though finding one in a few minutes isn't saving anywhere close to that much time, I have another one in as many days...
[CODE]
got assignment: exp=57620203 bit_min=71 bit_max=72
Starting trial factoring M57620203 from 2^71 to 2^72
k_min = 20489195787060
k_max = 40978391579682
Using GPU kernel "barrett79_mul32"
found 0 factor(s) already
class | candidates | time | ETA | avg. rate | SievePrimes | CPU wait
876/4620 | 1.07G | 11.111s | 2h23m | 96.07M/s | 7396 | 6.06%
M57620203 has a factor: 3169216471470499491337
found 1 factor for M57620203 from 2^71 to 2^72 (partially tested) [mfaktc 0.18 barrett79_mul32]
[B]estimated total time spent: 3m 24.699s[/B]
[/CODE]

[QUOTE]Let's see ... M15xxxxxx, 58 to 65 bits, these days might take half an hour ... no idea, but maybe a good gpu in minutes ...[/QUOTE]

Just for giggles I setup [URL="http://www.mersenne.org/report_exponent/?exp_lo=15000607&exp_hi=&B1=Get+status"]M15000607[/URL]: ~ 15 minutes on my 580 (with 4 other workers running concurrently)

[CODE]
got assignment: exp=15000607 bit_min=58 bit_max=65
Starting trial factoring M15000607 from 2^58 to 2^65
k_min = 9607290000
k_max = 1229733175044
Using GPU kernel "75bit_mul32"
class | candidates | time | ETA | avg. rate | SievePrimes | CPU wait
89/4620 | 60.82M | 0.956s | [B]14m58s[/B] | 63.62M/s | 11896 | 3.01%
[/CODE]

lorgix 2012-06-10 22:23

I just saved my first 2 LL tests near the wavefront. (GPU272)

M61665733 has a factor: 1242867428216309008697

k= 2*2*11*229033092049

c10ck3r 2012-06-14 18:46

M995699 has a factor: 714989201981049862823489485269929
k=2^2 x 13 x 61 x 3301 x 24001 x 2033287 x !702,642,949!
I *THINK* this is a B-S factor since it was found with B1=10M B2=250M E=12
109.14 bits :) My first above 100 bits!

firejuggler 2012-06-18 23:05

I know it is useless but still
M8803577 completed P-1, B1=105000, B2=1916250, E=6
P-1 found a factor in stage #1, B1=105000.
UID: firejuggler, M8803573 has a factor: 589495498411470532681
k=2^2*3*5*2857*4831*40429

last pm1 was @ B1=40000, B2=B1, so it didn't need 'much' more to get it

flashjh 2012-06-19 03:23

[QUOTE=firejuggler;302622]I know it is useless but still
M8803577 completed P-1, B1=105000, B2=1916250, E=6
P-1 found a factor in stage #1, B1=105000.
UID: firejuggler, M8803573 has a factor: 589495498411470532681
k=2^2*3*5*2857*4831*40429

last pm1 was @ B1=40000, B2=B1, so it didn't need 'much' more to get it[/QUOTE]
Wow, that wasn't missed by much at all the first time!

c10ck3r 2012-06-23 17:18

M115674281 has a factor: 40339344939109680617
M115661719 has a factor: 40122317215718082599
found consecutively on a system that takes 129 mins for these assignments for full length, 17 mins apart :)

firejuggler 2012-06-24 19:30

[code]
[Sun Jun 24 21:24:31 2012]
P-1 found a factor in stage #2, B1=100000, B2=1925000.
UID: firejuggler, M7930861 has a factor: 6680754188444328044071639,
[/code]
factor is 82.466 bit. Rather large for this exponent.
k=3 × 19 × 137 × 2161 × 80789 × 308939

c10ck3r 2012-06-25 00:00

M3243839 has a factor: 802301222696287988092559711
M3244867 has a factor: 556924867429225023624318383
M3245537 has a factor: 25502181971466624689
90 bits k=5 x 71 x 97 x 2837 x 233159 x 5429209
89 bits k=59 x 89 x 1433 x 518717 x 21986243 , and
65 bits, k=2 ^ 3 x 11 x 47 x 53 x 17922739 , respectively.
Found using P-1 bounds B1=1M B2=30M, all found stage 2, no B-S.

firejuggler 2012-06-30 07:38

[Sat Jun 30 02:28:44 2012]
P-1 found a factor in stage #1, B1=110000.
UID: firejuggler, M9251881 has a factor: 126328218334013927786152730351

96.673 bit, k=5^2*31*139*1867*9247*56827*95621

dabaichi 2012-07-03 08:02

Bad TF results?
 
1 Attachment(s)
[URL="http://www.mersenne.org/report_exponent/?exp_lo=601983997&exp_hi=10000&B1=Get+status"]M601983997[/URL] has a factor: 60136908979114760311 (65.705 bits)
[URL="http://www.mersenne.org/report_exponent/?exp_lo=601986001&exp_hi=&B1=Get+status"]M601986001[/URL] has a factor: 41955526838838866881 (65.185 bits)

Both were found by trial factoring using Prime 95. However, the interesting part is that both had been TFed using mfakto up to 67 bits, but reported no factors. It leads me to think is it necessary to double check trial factoring results?

axn 2012-07-03 08:35

[QUOTE=dabaichi;303932]It leads me to think is it necessary to double check trial factoring results?[/QUOTE]

It depends. If it is a reproducible error (i.e. bug) in mfakto, then maybe. If it is a hardware issue, then no. AFAICT, "gpu 2 72" has been finding the expected number of factors.

Dubslow 2012-07-03 08:36

So someone should rerun those with mfakto, but I'd only be worried if they were different users.

LaurV 2012-07-03 09:54

Good points axn and Dubslow.
It may be a hardware error, or some guys who love the credit more than the truth.

FWIW, mfaktc v0.18 finds both factors in a blink of an eye, with three different settings: 0 to 70, 65 to 70 and 65 to 66 bits (the difference is important, as for example in the first case he is sieving all 0-69 range in a single step).

PageFault 2012-07-07 01:32

Found another one ... [URL="http://mersenne-aries.sili.net/exponent.php?exponentdetails=70002461"]M70002461[/URL]

[CODE]P-1 found a factor in stage #2, B1=810000, B2=21060000.
UID: PageFault/boxen_01, M70002461 has a factor: 10006641404605893135455599[/CODE]

k = 3 * 7 * 11 *17 * 1063 * 4931 * 3472289

Bdot 2012-07-07 20:17

[QUOTE=dabaichi;303932][URL="http://www.mersenne.org/report_exponent/?exp_lo=601983997&exp_hi=10000&B1=Get+status"]M601983997[/URL] has a factor: 60136908979114760311 (65.705 bits)
[URL="http://www.mersenne.org/report_exponent/?exp_lo=601986001&exp_hi=&B1=Get+status"]M601986001[/URL] has a factor: 41955526838838866881 (65.185 bits)

Both were found by trial factoring using Prime 95. However, the interesting part is that both had been TFed using mfakto up to 67 bits, but reported no factors. It leads me to think is it necessary to double check trial factoring results?[/QUOTE]

Good catch. I had already asked James to go over his factor DB to see if there are P-1 results that fall into a range that mfakto cleared as NF. I did not think of someone rechecking using prime95 ...

[QUOTE=axn;303937]It depends. If it is a reproducible error (i.e. bug) in mfakto, then maybe. If it is a hardware issue, then no. AFAICT, "gpu 2 72" has been finding the expected number of factors.[/QUOTE]
In GPU272 I'm even 5% ahead of the expected (I know, law of small numbers).
[QUOTE=Dubslow;303939]So someone should rerun those with mfakto, but I'd only be worried if they were different users.[/QUOTE]
I'll definitely check different settings for that tomorrow.

Would it be useful to add a checksum in the result lines, just to make sure it's not modified before submittal but we (I) really have to deal with a bug? At first, that checksum would only be recorded, but later the server could also verify it ...


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