[QUOTE=Uncwilly;234155]Here is a current summary of the current guesses. I have retained some data from the predict 47 thread (where there was no new data).
[CODE]Damian 45,000,000
Storm5510 46,500,000 9/15/2010
Primeinator 47,300,000 10/1/2009
jasong 48,200,000
ATH 49,000,000 3/1/2010
Raman 50,000,000
MiniGeek 50,000,000 9/1/2009
ixfd64 50,000,000 2/1/2010
uigrad 51,500,000 8/1/2009
McDuck 54,000,000 6/24/2010
firejuggler 57,500,000
10metreh 59,278,411 6/30/2011
davieddy 60,000,000 1/1/2012
joblack 60,500,000
MoooMoo 75,860,000 5/1/2013
XYYXF 88,000,000 11/1/2011
nngs 90,087,850
Terrance Law 98,000,000 5/1/2011
Uncwilly 332,192,831 2/12/2011
henryzz 8/31/2009
ET 12/20/2012
[/CODE]For the fun of it here are some calculations based upon data from the GIMPS era:
[CODE]Last discovery: 4/12/09
LD plus ave. gap 4/24/10
above
+1/2 standard deviation 9/7/10
+average dev 12/2/10 <--- closest date
+1 std dev 1/20/11
+1.5 std dev 6/5/11
LD + max gap 9/26/11[/CODE][/QUOTE]
You forgot to include my guess earlier:
[url]http://www.mersenneforum.org/showpost.php?p=213821&postcount=87[/url]

[quote]I have looked at the "expected new primes" < 79,300,000 for
April 2001,2004,2007 and 2010.
[URL]http://web.archive.org/web/*/http://mersenne.org/status.htm[/URL]

From these figures, I deduce:

01 - 04 we expected 1.64 (found 2)
04 - 07 we expected 1.28 (found 4)
07 - 10 we expected 0.69 (found 3)

Note that expecting 0.69 corresponds to an even chance
of finding one or more.

I would guess that finding M48 before 2015 is a toss up.

[/quote]If by toss-up you mean a 50-50 chance, I disagree.

I think sometime early in 2011, though I don't know in what range
it will be found.

And aren't we all assuming the infinitude of the Mersenne Primes?

[quote]If I may go off on a fairly wild tangent here, I have a friend who tried sieving numbers of the form k*2^n+1, where 2^n+1 was a Fermat number. Sometimes he would find factors of 7 digits or more which would wipe out a huge chunk of the remaining equations in one fell swoop(as much as 1/3rd of the numbers in a sieve file). Maybe there are properties to the factors of the Mersenne numbers that we haven't discovered which could shed some light on why the last 8 Mersenne primes are so close together. Possibly even the sort of thing which could help find gigantic primes in general, since sieving is a major part of prime-finding.[/quote]I agree absolutely, but the solution will be mathematical not arithmetical.

[quote]If He exists outside of time, why did He wait until something was about to happen before "realizing" it and then changed things at almost the last moment?

I believe He extended His noodly appendage at the moment of creation to make sure everything worked out correctly.
[/quote]I recognize the humor, but you really have the beginnings of a proof
of his non-existence. In the religious intolerance thread, perhaps?

For M47: soon.

For M48: ~52,100,000 in 12/2011-2/2012.

For M49 (to jump the gun): sooner or later.

Here is a current summary of the current guesses.
[FONT="Fixedsys"]
Damian.........45,000,000
Storm5510......46,500,000....[COLOR="Red"][strike]09/15/2010[/strike][/COLOR]
Primeinator....47,300,000....[COLOR="Red"][strike]10/01/2009[/strike][/COLOR]
jasong.........48,200,000
ATH............49,000,000....[COLOR="Red"][strike]03/01/2010[/strike][/COLOR]
Raman..........50,000,000
MiniGeek.......50,000,000....[COLOR="Red"][strike]09/01/2009[/strike][/COLOR]
ixfd64.........50,000,000....[COLOR="Red"][strike]02/01/2010[/strike][/COLOR]
uigrad.........51,500,000....[COLOR="Red"][strike]08/01/2009[/strike][/COLOR]
davar55 .......52,100,000....12/31/2011
McDuck ........54,000,000....[COLOR="Red"][strike]06/24/2010[/strike][/COLOR]
firejuggler....57,500,000
10metreh.......59,278,411....06/30/2011
davieddy.......60,000,000....01/01/2012
joblack........60,500,000
Oddball........78,000,000....01/01/2013
MoooMoo........75,860,000....05/01/2013
XYYXF..........88,000,000....11/01/2011
nngs...........90,087,850
Terrance Law...98,000,000....05/01/2011
Uncwilly......332,192,831....02/12/2011
henryzz......................[COLOR="Red"][strike]08/31/2009[/strike][/COLOR]
ET_..........................12/20/2012
Yzzyx .......................01/19/2038[/FONT]


For the fun of it here are some calculations based upon data from the GIMPS era:
[CODE]Last discovery: 4/12/09
LD plus ave. gap 4/24/10
above
+1/2 standard deviation 9/7/10
+average dev 12/2/10
+1 std dev 1/20/11 <--already past
+1.5 std dev 6/5/11
LD + max gap 9/26/11[/CODE]
All exponents below 37,591,483 have been tested at least once.

My standing prediction (from another thread): [url]http://www.mersenneforum.org/showpost.php?p=86896&postcount=3[/url]

55,555,543

May 5, 2012 (2+0+1+2 = 5)

I have added those posted and went as far back as I could (older threads) and entered everything that was larger or later than the to-date status of 37591483 on 1/24/2011

[QUOTE=10metreh;176246]Well, we don't know "M47" is prime, but we have strong evidence for it, so it's time to have a guess at M48. My guess: about 59M, January 2011. :curtisc:

(Mods: Feel free to delete this thread if "M47" turns out not to be prime.)[/QUOTE]
Seems like it is prime.
OTOH it is now March 2011.
I have sussed a neat way of estimating the expected time
of discovery of the next Mersenne prime:

On the "Classic" GIMPs progress page the expected new primes
below 79.3M decreases by .001 in somewhat
over 2 days.

I'll wager you 50/50 that we'll find a new MP before 2015.

David

[QUOTE=davieddy;255109]On the "Classic" GIMPs progress page the expected new primes below 79.3M decreases by .001 in somewhat over 2 days.[/QUOTE]
Well the here is the recent history on that:
2010-10-25 1.34
2010-11-22 1.33
2010-12-25 1.31
2011-01-11 1.31
2011-02-05 1.30
2011-03-07 1.28

[QUOTE=Uncwilly;255110]Well the here is the recent history on that:
2010-10-25 1.34
2010-11-22 1.33
2010-12-25 1.31
2011-01-11 1.31
2011-02-05 1.30
2011-03-07 1.28[/QUOTE]

THX for this info.
But note that 0.01 = 10 x 0.001

David

[QUOTE=davieddy;255179]But note that 0.01 = 10 x 0.001[/QUOTE]
2008-10-25 1.747
2008-12-03 1.719
2009-10-25 1.528
2010-05-11 1.420
2010-10-25 1.342
2010-11-22 1.328
2010-12-25 1.314
2011-01-11 1.306
2011-02-05 1.295
2011-03-07 1.281

FWIW

[QUOTE=Uncwilly;255181]

FWIW[/QUOTE]

[url=http://www.youtube.com/watch?v=f5M_Ttstbgs]For what it's worth[/url]

Damn close to my favourite record of all time.

David

[QUOTE=Uncwilly;255181]
2008-10-25 1.747
2008-12-03 1.719
2009-10-25 1.528
2010-05-11 1.420
2010-10-25 1.342
2010-11-22 1.328
2010-12-25 1.314
2011-01-11 1.306
2011-02-05 1.295
2011-03-07 1.281

FWIW[/QUOTE]
So we expected 0.466 primes in about 860 days.
So 0.001 prime in just under two days.
Undrstandably, the current expected discovery rate has
dropped slightly: I think 50M turned out to be a major
hurdle allocation-wise.
Note however that the current expected rate of a new
prime every 6 years is sustainable if we achieve a 20% increase
in computing per year. Not too much to expect from Mr Moore:smile:

David

Note also that the expected time before the next prime
is discovered is 6 years from NOW.

Some of the predictions on Chris Caldwell's instructive
"Where is the next MP?" page are beginning to look
distinctly optimistic ;)
(The same could be said of just about all the predictions
in this thread!)

We just past May 22. This was the date that using the 'forecast' function (in Excel) a new prime would be found. (All data in the post concerns only the GIMPS era).
In about 2 weeks we will hit June 5. That is the date of last discovery of a prime + the average gap + 1.5 std dev.

And we should be hitting a new prime at around 49,000,000 (according to my calcs). And we have just more that half of those LL'ed.

George is on vacation and having a problem with networking.

Watch out.

[QUOTE=Uncwilly;262121]
(snip)
And we should be hitting a new prime at around 49,000,000 (according to my calcs). And we have just more that half of those LL'ed.

George is on vacation and having a problem with networking.

Watch out.[/QUOTE]
:devil: If I wanted to be paranoid, G isn't on vacation...he's visiting the discoverer of M48!
Crunch, crunch.....P-1 is knocking out candidates in the M53 range noticeably faster than my first LL tests...though my sample from 1 set of computers is pretty small, under 1000GHz days still.

[QUOTE=Uncwilly;262121]We just past May 22.
...
And we should be hitting a new prime at around 49,000,000 (according to my calcs). And we have just more that half of those LL'ed.

George is on vacation and having a problem with networking.

Watch out.[/QUOTE]

Unfortunately, that's the gambler's fallacy, that a prime should be 'due' because of any reason. All you can do is say that right now, we can expect to have x primes by such-and-such date or exponent. As of when the last prime was found, apparently those were around May/June and 49,000,000. If, for simplicity, that was 12 months and 5M, now it's another ~>12 months and ~>5M before you expect one.

Just for fun.
49M 2013

[QUOTE=wreck;262157]Just for fun.
49M 2013[/QUOTE]

To quote Manuel cmd "Me no understand. I'm comer fromer Italia"

David

49M = M49????

Que?

[QUOTE=Mini-Geek;262147]49,000,000. If, for simplicity, that was 12 months and 5M, now it's another ~>12 months and ~>5M before you expect one.[/QUOTE]

For realism, make that 60 months and 25M

Poisson George Wagstaff

[QUOTE=davar55;243235]For M48: ~52,100,000 in 12/2011-2/2012.

For M49 (to jump the gun): sooner or later.[/QUOTE]

May I change my original guess and make
a real two-pronged guess?

For M48: ~77,000,000 by 6/2012 reached by luck

For M49: (big gap to) ~205,000,000 by 2/2015 reached analytically

No analytic reason, just intuited from the recent clustered values
and my estimate that the sequential ratios of consecutive
mersenne exponents hovers around 1.500000.

Dear Davar
 

With nutters like you around, who needs...

David

[QUOTE=wreck;262157]Just for fun.
49M 2013[/QUOTE]

I think he means M48 will be M(49 xxx xxx) and found in 2013, in a SWAG -- Sophisticated, Wild-Assed Guess

Can't say I even know a little, you can look at plots yourself and guess...I'd be surprised if M48 > M(60 000 000) and M49 > M(100 000 000), but I'm expecting half a dozen primes in that range....

M176,863,549 in year 2052
 

My guess is

[URL="http://www.mersenneforum.org/showpost.php?p=260849&postcount=1"]M176,863,549 in year 2052[/URL]

:smile::tantrum::cmd:

[QUOTE=Christenson;262177]
Can't say I even know a little, you can look at plots yourself and guess...I'd be surprised if M48 > M(60 000 000) and M49 > M(100 000 000), but I'm expecting half a dozen primes in that range....[/QUOTE]

Big Hmmm there.

Without forgetting that I can sometimes miss a joke/point at my
age/state of sobriety, I think the number of non-Mersenne primes
between 2^(60M) and 2^(100M) is more than 6.

If you mean the 49th Mersenne prime to be discovered will have
skipped 6 others (a la M45(?),M46(?) or M29), I would be staggered.

The last 7 gaps have been shorter than expected. < 1.3 ratio is
~ a 50/50 proposition. BUT:
7+ heads in a row occurs once in 256 coin tosses, so the lucky
streak of the last 8 MP discoveries is not freakish enough to
warrant dismissing Wagstaff's conjecture.

David

[QUOTE=wreck;262157]Just for fun.
49M 2013[/QUOTE]I will assume that you mean Jan 1, 2013[QUOTE=davar55;262166]For M48: ~77,000,000 by 6/2012 reached by luck

For M49: (big gap to) ~205,000,000 by 2/2015 reached analytically[/QUOTE]Noted[QUOTE=aketilander;262192]M176,863,549 in year 2052[/QUOTE]Noted

Expected new Mprimes <79.3M
 

[QUOTE=Uncwilly;255181]2008-10-25 1.747
2008-12-03 1.719
2009-10-25 1.528
2010-05-11 1.420
2010-10-25 1.342
2010-11-22 1.328
2010-12-25 1.314
2011-01-11 1.306
2011-02-05 1.295
2011-03-07 1.281

FWIW[/QUOTE]

2011-05-26 1.244

~ 3.7% chance of of finding a new Mprime in 80 days.

Note to Gambler's Fallacy fans, the
discovery of a prime in 2009 made no differnce
to the expected new primes.

David

[QUOTE=Christenson;262123]
Crunch, crunch.....P-1 is knocking out candidates in the M53 range noticeably faster than my first LL tests...though my sample from 1 set of computers is pretty small, under 1000GHz days still.[/QUOTE]

If, by "knocking out" you mean finding a factor, that is the whole
purpose of P-1. I wonder whether enough folk are aware of it.

Not only does TF and P-1 reduce the number of LL tests, it enhances
the probability of the remaining candidates being prime accordingly,
leaving the expected number of primes in a range unchanged, and
increasing incentive to play the LLtest lottery!

David

8 factors, 562 GHz-Days by P-1, 906 GHz days for 11 first time LL tests, which will have to be repeated for another 906 GHz days. P-1 is removing LL candidates from both LL tests in a little less time than it takes to do the first LL tests... but Mr Wagstaff would remind me my sample is tiny....I'm not doing nearly so well by TF, beginning to think that the my policy of going to higher bit levels isn't effective until lower bit levels are exhausted...

[QUOTE=Christenson;262500]8 factors, 562 GHz-Days by P-1, 906 GHz days for 11 first time LL tests, which will have to be repeated for another 906 GHz days. P-1 is removing LL candidates from both LL tests in a little less time than it takes to do the first LL tests... but Mr Wagstaff would remind me my sample is tiny....I'm not doing nearly so well by TF, beginning to think that the my policy of going to higher bit levels isn't effective until lower bit levels are exhausted...[/QUOTE]

As I said above, P-1 is worthwhile (and should preferably be done
before the first LL test.

As for sample size, GHzDays/LLtest is ~ constant, as is P-1(?)

8 factors from 100(???) tests?
Standard deviation for the binomial distribution is SQR(8*92/100) =2.7

Statistically significant sample size I would suggest!

David

And yes, it's obviously worth TFing upwards :smile:

PS WBlipp is on board ATM.
He is an expert statistician, and tell you more
than you need to know!
With that in mind, I shall refine my "analysis" of
"What does 8 successes from 100 trials say about
the population mean and its standard deviation?"

In due course!

No now:
The best guess is that the population mean is 8 per 100
and the sd is SQR(8*92/99).

[QUOTE=davieddy;262502]
The best guess is that the population mean is 8 per 100
and the sd is SQR(8*92/99).[/QUOTE]

This needs wording more carefully I think.
I'm trying to estimate p(find a factor in one trial) from 100 trials,
and sd refers to the sd of this guess.

I'm possibly thinking about the "population" being a huge number
of sets of 100 trials, but I'm sure my numerical answer is close to the mark.


More later.

David

Concluded a night or two ago that it was better to search breadth-first on TF, rather than depth-first, since it will eliminate more LL tests sooner. If the lower bit level finishes, then do the next one...
When I wrote my previous post, I was up to 125 P-1 tests...I get estimates from P95 like "Chance of finding a factor is an estimated 5.96%".

[QUOTE=davieddy;262358]2011-05-26 1.244

~ 3.7% chance of of finding a new Mprime in 80 days.

[/QUOTE]

2011-06-22 1.231

1.3% chance in 27 days.

Too early to say, but my suggestion that the expected
time for a new MP of ~6 years is sustainable, might have some
merit!

David

PS I know this an exciting and changing time for GIMPS ATM,
but what is needed to sustain a prime every 6 years is a 20%
increase in GIMPS computing power per year.

"Come on you Yellows!".
(A Norwich City chant in case anyone thought I meant Chinamen)

We've had a 100x increase in TF power, by the GPUs, which gives about 10% decrease in the numbers of LL tests to do....we need to solidify that and then get the GPUs working on LL tests, too....

Any kind soul running mfaktc care to help?
 

I'm about to LL M45275047.

TFed to 68. No P-1
I would be interested to P-1 it myself; (will this happen automatically?
Soon find out).

But would anyone care to TF it higher on a GPU?

If you find no factor, I'll make sure you share some credit if it's prime.
If you do, you will have saved me 2 month's "work"!

David

[QUOTE=davieddy;264537]I'm about to LL M45275047.

TFed to 68. No P-1
I would be interested to P-1 it myself; (will this happen automatically?
Soon find out.)[/QUOTE]
It should automatically do P-1, yes. If you don't have enough RAM to do a good job (ie, 300MB or more) then I'll offer to do the P-1 on it. I've been doing a bunch of P-1 in the 40-50M range recently. I have a machine with 16GB of RAM, with 12GB available to GIMPS. Makes for a great P-1 machine. :)

[QUOTE=davieddy;264537]
But would anyone care to TF it higher on a GPU?

If you find no factor, I'll make sure you share some credit if it's prime.
If you do, you will have saved me some work!

David[/QUOTE]
I would, but I haven't got a suitable GPU.

[QUOTE=KingKurly;264538]It should automatically do P-1, yes. If you don't have enough RAM to do a good job (ie, 300MB or more) then I'll offer to do the P-1 on it. I've been doing a bunch of P-1 in the 40-50M range recently. I have a machine with 16GB of RAM, with 12GB available to GIMPS. Makes for a great P-1 machine. :)

I would, but I haven't got a suitable GPU.[/QUOTE]

THX. I've got 1GB RAM.

Half the point of my inviting collaboration, was to suggest that
since ATM GPUs do TF like shit off a shovel, their most
constructive contribution to GIMPS is currently assisting CPUs
in their struggle to do LL testing. Since they may do P-1 and/or
LL in the near future, there is little point in finding "cheap" factors
above say 60M. It will be 2 years before the LL wavefront reaches
that point, so speeding up it's advance is obviously GIMPS top
priority.

David

[QUOTE=davieddy;264537]I'm about to LL M45275047.

TFed to 68. No P-1
I would be interested to P-1 it myself; (will this happen automatically?
Soon find out).

But would anyone care to TF it higher on a GPU?

If you find no factor, I'll make sure you share some credit if it's prime.
If you do, you will have saved me 2 month's "work"!

David[/QUOTE]

If you haven't started your LL yet, I'll take it up some for you. I've got a test completing in about 40 min, or another in about 70 min, and I can move it up for you. I can TF it up to 73 in about 6 - 7 hrs.

Doug

[QUOTE=drh;264562]If you haven't started your LL yet, I'll take it up some for you. I've got a test completing in about 40 min, or another in about 70 min, and I can move it up for you. I can TF it up to 73 in about 6 - 7 hrs.

Doug[/QUOTE]

Great! Many thanks.
It will start tommow afternoon, (although I could stop it if
you find a factor). With no P-1 done 5 bit levels should give you
a 5/68 chance of a factor.

I await news, or perhaps the server will tell me if you do.

David

[QUOTE=davieddy;264565]Great! Many thanks.
It will start tommow afternoon, (although I could stop it if
you find a factor. With no P-1 done 5 bit levels should give you
1/14 chance of a factor.

I await news, or perhaps the server will tell me if you do.

David[/QUOTE]

If you release the exponent, I'll pick it up right now, and let you know when it's done before I release it back so you can LL it ... will that work for you?

[QUOTE=drh;264567]If you release the exponent, I'll pick it up right now, and let you know when it's done before I release it back so you can LL it ... will that work for you?[/QUOTE]
M45275047 released.Is this manouvre strictly necessary?
Pick it up before someone else does!

[QUOTE=davieddy;264568]M45275047 released.Is this manouvre strictly necessary?
Pick it up before someone else does![/QUOTE]

The server is not letting me pick it up, at least not yet. Maybe I need to wait for a refresh at the top of the hour, otherwise, if I can't get it, take it back and let me know. I'll keep trying. I'll try running it without an assignment ... no credit.

[QUOTE=drh;264569]The server is not letting me pick it up, at least not yet. Maybe I need to wait for a refresh at the top of the hour, otherwise, if I can't get it, take it back and let me know. I'll keep trying. I'll try running it without an assignment ... no credit.[/QUOTE]

Well, this really sucks ... as soon as you released it, it got assigned to "chicago454" for LL. Really didn't think it would happen that quick :(

[QUOTE=drh;264570]Well, this really sucks ... as soon as you released it, it got assigned to "chicago454" for LL. Really didn't think it would happen that quick :([/QUOTE]

Hmmm. But nothing lost - plenty of other exponents.
I thought they were made available at 2400 UTC.

Perhaps something can advise us on this attempt at collaboration.
One would hope one didn't have to be furtive about it!
I don't want to experiment too much until my current
exponent safely completes tommorrow.
It's just that the smaller the exponent, the quicker the LL
and the greater the probability of it being prime.

If you can get a small one when available, (2400 UTC),
you could tell me and I'll ask to test it.

[QUOTE=davieddy;264571]Hmmm. But nothing lost - plenty of other exponents.
I thought they were made available at 2400 UTC.

Perhaps something can advise us on this attempt at collaboration.
One would hope one didn't have to be furtive about it!
I don't want to experiment too much until my current
exponent safely completes tommorrow.
It's just that the smaller the exponent, the quicker the LL
and the greater the probability of it being prime.

If you can get a small one when available, (2400 UTC),
you could tell me and I'll ask to test it.[/QUOTE]

Looking at the [FONT=Tahoma][SIZE=4][FONT=Verdana][SIZE=2]PrimeNet Activity Summary page, it appears that the best I could probably do is one of the 1421 available TF's in the 58M range. If I can get one of those, would you be interested?[/SIZE][/FONT][/SIZE][/FONT]

[QUOTE=drh;264573]Looking at the [FONT=Tahoma][SIZE=4][FONT=Verdana][SIZE=2]PrimeNet Activity Summary page, it appears that the best I could probably do is one of the 1421 available TF's in the 58M range. If I can get one of those, would you be interested?[/SIZE][/FONT][/SIZE][/FONT][/QUOTE]Thanks, but no thanks!

To LL 58M now goes completely against my "reasoning" in post #135.

I expect to be assigned another ~ 45M test at 0145 UTC.

I'm sure if you TFed it you could get credit manually, although
ATM it seems that Primenet doesn't appreciate mfaktc or GPUs yet.

I feel (as I expect you do) that more user-friendliness would increase
participation in GIMPS.

David

[QUOTE=davieddy;264580]Thanks, but no thanks!

To LL 58M now goes completely against my "reasoning" in post #135.

I expect to be assigned another ~ 45M test at 0145 UTC.

I'm sure if you TFed it you could get credit manually, although
ATM it seems that Primenet doesn't appreciate mfaktc or GPUs yet.

I feel (as I expect you do) that more user-friendliness would increase
participation in GIMPS.

David[/QUOTE]

Totally understand, and agree. Do you know if it's possible to get credit without an assignment? I always request an assignment first, when I do my manual work.

Thanks,
Doug

From another thread here, regarding axon, it seems the server is rather liberal about granting credit for work that wasn't assigned, no worry there....

Do you need another exponent TF'ed? I have a reasonably fast GPU that I'm willing to ask to extend the TF range, though it may be busy for the next 20-30 hours on a little job for the Billion Digit folks....and it may take six hour for me to read your reply....I'll just feed it a manual assignment. I can PM the result, as well as report it to the server.

Note that the odds of my finding a factor aren't good at a high bit level, but I don't mind trying.

8 hours to go on that piece of the "little" job...I'm willing to insert a TF command to execute at that point.

OK: Take 2
 

M45705851 TFed to 68 bits. B1=480000 B2=4080000.

Further TF welcome. If the two of you are willing to do
5 more bits, the fairest division of labour is 68-72 and 72-73.

I'm afraid the P-1 reduces the expectation of a factor from 5/68
to more like 5%.

I've got 5 hours to go before I can start to LL it, but don't panic:smile:

David

PS Not going to risk "releasing" it this time!

Factor=0,45705851,68,72
Begins in 4 hours on my GTX 440.
This isn't the fastest GPU in the world....just the best my slightly undersized power supply for my AMD Phenom II x6 can support. When i get up in 7-8 hours, I'll report how it's going. It's 23:43 local (E coast US) time, which I think is GMT+5.

[QUOTE=Christenson;264617]It's 23:43 local (E coast US) time, which I think is GMT+5.[/QUOTE]This time of year, it's GMT-4. When not in Daylight Savings Time, we're GMT-5.

Great to have a concrete case to discuss
 

[QUOTE=Christenson;264617]Factor=0,45705851,68,72
Begins in 4 hours on my GTX 440.
This isn't the fastest GPU in the world....just the best my slightly undersized power supply for my AMD Phenom II x6 can support. When i get up in 7-8 hours, I'll report how it's going. It's 23:43 local (E coast US) time, which I think is GMT+5.[/QUOTE]
Message received at 04:44 BST = 03:44 GMT(UTC)

My best iteration times are pretty close to those of 2GHz day/day.
(Celeron440 @2Ghz).

I would estimate that it would take it over a day
to TF 68-69. I await news of your progress with interest!

BTW Prime95 says the probability of being prime is 1/378756,
but I'm not sure whether this takes P-1 into account. George?

Each 1% improvement in these odds converts to a larger incentive
for folk to take on [B]and finish[/B] LL tests!

4 extra bits of TF should make our Mexponent the single most
likely to be prime. Poaching excepted.

David

[QUOTE=davieddy;264636]BTW Prime95 says the probability of being prime is 1/378756,
but I'm not sure whether this takes P-1 into account. George?[/QUOTE]

If it does at all, it could only be in roughest terms, since Prime95 doesn't keep track of what bounds were used in P-1 when you doublecheck/LL, just a 0 for "not-done" and a 1 for "done". So if it was done with generous bounds, you can expect it to be significantly more likely to be prime than stated.

From my "results.txt":
no factor for M45705851 from 2^68 to 2^69 [mfaktc 0.17 barrett79_mul32]
no factor for M45705851 from 2^69 to 2^70 [mfaktc 0.17 barrett79_mul32]
no factor for M45705851 from 2^70 to 2^71 [mfaktc 0.17 barrett79_mul32]

From my "worktodo.txt":
Factor=0,45705851,71,72
Factor=0,45705851,72,73

From my console, just a few minutes before this post:
no factor for M45705851 from 2^70 to 2^71 [mfaktc 0.17 barrett79_mul32]
tf(): total time spent: 2h 45m 42.719s

tf(45705851, 71, 72, ...);
k_min = 25830207618600
k_max = 51660415237314
Using GPU kernel "barrett79_mul32"
......
class | candidates | time | avg. rate | SievePrimes | ETA | avg. wait
193/4620 | 1.12G | 22.696s | 49.43M/s | 56419 | 5h47m | 234us


From my calculations:
5 factor candidates at ~70 bits =~ 5/70 = 1/14 chance of finding a factor, thus saving you the LL testing. Cost of test will be ~20 hours, for about 30GHz days credit. This improves your odds of having M48 insignificantly, from miniscule to miniscule.
Mersenne-aries.sili.net tells us:
73.3GHz days for the LL (so 146.6 days work will need to be done if no factor is found)
40.5Ghz days for TF(68,73).
The classical calculaton says we are well above optimum TF for GHz-Days granted, even ignoring any P-1. An argument could be made for TF to 74 bits, assuming my GPU effort for a GHz-Day is 1/10th the effort of a CPU GHz-day. (This is based on the idea that it is a mid-range card. Someone who has a top-end card could carry out another 2-3 bits for the same wall-calendar effort.)

Many thanks
 

[QUOTE=Christenson;264641]
From my calculations:
5 factor candidates at ~70 bits =~ 5/70 = 1/14 chance of finding a factor, thus saving you the LL testing. Cost of test will be ~20 hours, for about 30GHz days credit. This improves your odds of having M48 insignificantly, from miniscule to miniscule.[/QUOTE]

From [B]my[/B] calculations:
Ignoring P-1 (see Minigeek's post) and assuming
that the probability of finding one or more factors between
2^X and 2^(X+1) is 1/X:

Probability of no factor between 2^X and 2^(X+1) is (X-1)/X.
Probability of no factor between 2^68 and 2^73 is 67/72.

oldminiscule = 1/378756 = 67/72 * newminiscule

newminiscule = 1/352454

Us toilers derive encouragement from such things:smile:

David

[QUOTE=davieddy;264648]Probability of no factor between 2^X and 2^(X+1) is (X-1)/X.[/QUOTE]

[TEX]\sum{k((x-1)/x)} [/TEX] where k is 2^(x-original x) should give the value between any 2 x then no ?

[QUOTE=davieddy;264537]I'm about to LL M45275047.

TFed to 68. No P-1
I would be interested to P-1 it myself; (will this happen automatically?
Soon find out).[/QUOTE]At that point::direction:Maybe these other posted can be moved to their own thread.

Your lack of perception is getting tiresome Uncle
 

Why do people do LL tests?

They hope to find M48, and arrive at sensible answers to the original
question.

Sure, this raises questions which would also be of interest elsewhere,
but you've got to post somewhere.

And you have been rude enough to suggest that I start too many
new threads.

Please go forth and multiply, and leave us in peace.

David

PS your words are close to incomprehensible,
and the mindless recording of wild guesses has long
outlived its entertainment value.


[QUOTE=Uncwilly;264651]At that point::direction:Maybe these other posted can be moved to their own thread.[/QUOTE]

[QUOTE=science_man_88;264650][TEX]\sum{k((x-1)/x)} [/TEX] where k is 2^(x-original x) should give the value between any 2 x then no ?[/QUOTE]

Do you mean (x-1)/x * x/(x+1) *.....*(y-1)/y = (x-1)/y
gives the probability of no factor between 2^x and 2^y?

If so, then yes.

David

[QUOTE=davieddy;264654]Do you mean (x-1)/x * x/(x+1) *.....*(y-1)/y = (x-1)/y
gives the probability of no factor between 2^x and 2^y?

If so, then yes.

David[/QUOTE]

I said k = 2^ what I said because the distance between the powers is doubled each time x is increased by 1 I'm not thinking maybe.

[QUOTE=davieddy;264653]
Sure, this raises questions which would also be of interest elsewhere,
but you've got to post somewhere.

And you have been rude enough to suggest that I start too many
new threads.
[/QUOTE]

That said, the digression is rapidly becoming worthy of a new thread.

Title might be "How can GPUs most effectively contribute to
the search for M48 at present?"

David

:explode::drama:

Davieddy:
I certainly thought this was a new thread direction.
I have been spending my day learning how to use the debugger in eclipse on mfaktc.
I suggest a title: Help with TF for small exponents.


You will do a P-1 prior to the LL if it hasn't been done and reported to the server. Mr P-1 encourages people to do a good job; I certainly have been finding factors via P-1 in fewer GHz-days than would be required for two LLs. But it's still a relatively infrequent thing, and, as noted elsewhere, some of my TF finds are reported on the stats pages as P-1 successes. Eventually we still have a lot of LL that has to be done.

From my console a few minutes ago:
no factor for M45705851 from 2^71 to 2^72 [mfaktc 0.17 barrett79_mul32]
tf(): total time spent: 5h 25m 16.423s

got assignment: exp=45705851 bit_min=72 bit_max=73
tf(45705851, 72, 73, ...);
k_min = 51660415237200
k_max = 103320830474628
Using GPU kernel "barrett79_mul32"
class | candidates | time | avg. rate | SievePrimes | ETA | avg. wait
0/4620 | 2.25G | 40.489s | 55.58M/s | 54668 | 10h47m | 474us
1/4620 | 2.25G | 40.450s | 55.63M/s | 54668 | 10h45m | 495us

I'll go ahead and ask it for 74 bits, just for fun...

Update, from my console:
[QUOTE]
no factor for M45705851 from 2^72 to 2^73 [mfaktc 0.17 barrett79_mul32]
tf(): time spent since restart: 1h 11m 21.076s
estimated total time spent: 10h 52m 21.266s

got assignment: exp=45705851 bit_min=73 bit_max=74
tf(45705851, 73, 74, ...);
k_min = 103320830474400
k_max = 206641660949257
Using GPU kernel "barrett79_mul32"
.....
class | candidates | time | avg. rate | SievePrimes | ETA | avg. wait
1605/4620 | 4.51G | 84.561s | 53.38M/s | 52693 | 14h40m | 572us
[/QUOTE]
The odds look very good that the LL test won't be wasted on M45705851.

[QUOTE=Christenson;264703]Update, from my console:

The odds look very good that the LL test won't be wasted on M45705851.[/QUOTE]
Or to put it another way, you TFing any more bits starts to look
like a waste of time.

Thanks again,

David

PS 2.8% of LLtest completed in 32 hours.
I ought to pay my 'puter more:smile:

Before we were so rudely interrupted...
 

[QUOTE=science_man_88;264658]I said k = 2^ what I said because the distance between the powers is doubled each time x is increased by 1 I'm not thinking maybe.[/QUOTE]

I have thought the same thing. Twice as many "candidates", yet (slightly)
less chance of any of them being a factor.

The answer is (roughly) that if a potential factor is twice as large
as another, it is half as likely to divide exactly.

David

It's official: TF has reached beyond a point of diminishing returns:
no factor for M45705851 from 2^68 to 2^69 [mfaktc 0.17 barrett79_mul32]
no factor for M45705851 from 2^69 to 2^70 [mfaktc 0.17 barrett79_mul32]
no factor for M45705851 from 2^70 to 2^71 [mfaktc 0.17 barrett79_mul32]
no factor for M45705851 from 2^71 to 2^72 [mfaktc 0.17 barrett79_mul32]
no factor for M45705851 from 2^72 to 2^73 [mfaktc 0.17 barrett79_mul32]
no factor for M45705851 from 2^73 to 2^74 [mfaktc 0.17 barrett79_mul32]

From the server:[FONT=monospace]
[/FONT]Processing result: no factor for M45705851 from 2^68 to 2^69 [mfaktc 0.17 barrett79_mul32][FONT=monospace]
[/FONT]CPU credit is 1.3080 GHz-days.[FONT=monospace]
[/FONT]Processing result: no factor for M45705851 from 2^69 to 2^70 [mfaktc 0.17 barrett79_mul32]
CPU credit is 2.6159 GHz-days.[FONT=monospace]
[/FONT]Processing result: no factor for M45705851 from 2^70 to 2^71 [mfaktc 0.17 barrett79_mul32][FONT=monospace]
[/FONT]CPU credit is 5.2319 GHz-days.[FONT=monospace]
[/FONT]Processing result: no factor for M45705851 from 2^71 to 2^72 [mfaktc 0.17 barrett79_mul32][FONT=monospace]
[/FONT]CPU credit is 10.4638 GHz-days.[FONT=monospace]
[/FONT]Processing result: no factor for M45705851 from 2^72 to 2^73 [mfaktc 0.17 barrett79_mul32]
CPU credit is 20.9275 GHz-days.[FONT=monospace]
[/FONT]Processing result: no factor for M45705851 from 2^73 to 2^74 [mfaktc 0.17 barrett79_mul32][FONT=monospace]
[/FONT]CPU credit is 41.8551 GHz-days

Back to the regular TF work.....which I would normally carry to just 70 bits on an exponent this size.

in general, TF should search breadth-first, as this maximises the number of exponents that won't have to be LL'ed for a given amount of work, since each new bit level costs twice the preceding bit level. But I'm willing to do special favors now and then....

[QUOTE=Christenson;264739]It's official: TF has reached beyond a point of diminishing returns:
no factor for M45705851 from 2^68 to 2^69 [mfaktc 0.17 barrett79_mul32]
no factor for M45705851 from 2^69 to 2^70 [mfaktc 0.17 barrett79_mul32]
no factor for M45705851 from 2^70 to 2^71 [mfaktc 0.17 barrett79_mul32]
no factor for M45705851 from 2^71 to 2^72 [mfaktc 0.17 barrett79_mul32]
no factor for M45705851 from 2^72 to 2^73 [mfaktc 0.17 barrett79_mul32]
no factor for M45705851 from 2^73 to 2^74 [mfaktc 0.17 barrett79_mul32]

From the server:[FONT=monospace]
[/FONT]Processing result: no factor for M45705851 from 2^68 to 2^69 [mfaktc 0.17 barrett79_mul32][FONT=monospace]
[/FONT]CPU credit is 1.3080 GHz-days.[FONT=monospace]
[/FONT]Processing result: no factor for M45705851 from 2^69 to 2^70 [mfaktc 0.17 barrett79_mul32]
CPU credit is 2.6159 GHz-days.[FONT=monospace]
[/FONT]Processing result: no factor for M45705851 from 2^70 to 2^71 [mfaktc 0.17 barrett79_mul32][FONT=monospace]
[/FONT]CPU credit is 5.2319 GHz-days.[FONT=monospace]
[/FONT]Processing result: no factor for M45705851 from 2^71 to 2^72 [mfaktc 0.17 barrett79_mul32][FONT=monospace]
[/FONT]CPU credit is 10.4638 GHz-days.[FONT=monospace]
[/FONT]Processing result: no factor for M45705851 from 2^72 to 2^73 [mfaktc 0.17 barrett79_mul32]
CPU credit is 20.9275 GHz-days.[FONT=monospace]
[/FONT]Processing result: no factor for M45705851 from 2^73 to 2^74 [mfaktc 0.17 barrett79_mul32][FONT=monospace]
[/FONT]CPU credit is 41.8551 GHz-days

Back to the regular TF work.....which I would normally carry to just 70 bits on an exponent this size.

in general, TF should search breadth-first, as this maximises the number of exponents that won't have to be LL'ed for a given amount of work, since each new bit level costs twice the preceding bit level. But I'm willing to do special favors now and then....[/QUOTE]

Please note that there is no need to do [b]both[/b] trial division [b]and[/b]
P-1 because running P-1 to limit B2 in step 2 will find any factors that
trial division would find up to 2 B2 p + 1.

[QUOTE=R.D. Silverman;264744]Please note that there is no need to do [B]both[/B] trial division [B]and[/B]
P-1 because running P-1 to limit B2 in step 2 will find any factors that
trial division would find up to 2 B2 p + 1.[/QUOTE]

p ~ 2^26
TF to 2^70
B2 needs to be 2^43 ~ 10^13

In our case B2 was 4080000

[QUOTE=R.D. Silverman;264744]Please note that there is no need to do [b]both[/b] trial division [b]and[/b]
P-1 because running P-1 to limit B2 in step 2 will find any factors that
trial division would find up to 2 B2 p + 1.[/QUOTE]

Whooops...didn't know the P-1 bounds...and my machines found two P-1 factors this weekend on unrelated regular primenet assignments.

However, I'm sure I've seen Prime95 say that the last bit of TF follows P-1, so some part of davieddy's math here doesn't quite add up. My question is if P-1 can be optimized, given the knowledge that TF has been done to a certain level...so it doesn't waste its time on possibilities that have been checked by TF.

[QUOTE=Christenson;264758] My question is if P-1 can be optimized, given the knowledge that TF has been done to a certain level...so it doesn't waste its time on possibilities that have been checked by TF.[/QUOTE]

No, but the opposite is true. Run P-1 first. Then don't bother running TF
on the bounds covered by P-1.

Now also:

Suppose you run P-1 to steps B1/B2. Thus, we are sure there are
no factors smaller than 2 B2 p + 1.

Now suppose we run TF to 2 K p + 1.

Ask yourself: what is the (conditional) probability of finding a factor
between 2 B2 p + 1 and 2 K p + 1 [b] given[/b] that P-1 failed?

The unconditional probability of finding a factor in [2 B2 p + 1, 2 K p + 1]
is easy to compute. In order that there be no factor in this interval
when P-1 [i]fails[/i], there has to be a certain condition present. If
2 L p + 1 is a divisor where B2 < L < K, then we know certain things
about L (i.e. it must have a prime power factor greater than B2).
This probability is not hard to compute. There may be other conditions as
well; I have not thought very deeply about this.

I think that you will find is that for "reasonable" B1 & B2, the chance
of P-1 missing a factor is not too high. (But my intuition might be wrong
here).

If I were doing things, rather than run both P-1 and TF, I would simply
increase the bounds on P-1 somewhat and give up on TF. This might
miss a few factors, but I think would save time overall. One would
need to compute the probabilities for various B1/B2 and TF bounds to
determine a good choice for the bounds, as well as compare the run-times.
I am not very motivated at the moment to do such analysis. It would
make a nice undergrad level research project.

It is possible to increase the B2 limit for P-1 with very little memory
penalty if one does not use a convolution based step 2. Of course, the
step 2 run time now becomes linear in B2.

[QUOTE=Christenson;264739]
Back to the regular TF work.....which I would normally carry to just 70 bits on an exponent this size.

in general, TF should search breadth-first, as this maximises the number of exponents that won't have to be LL'ed for a given amount of work, since each new bit level costs twice the preceding bit level. But I'm willing to do special favors now and then....[/QUOTE]

From the point of view of finding M48 asap, ALL factoring to date for
exponents > 60M is practically worthless.

I greatly appreciate your "special favor", and the enjoyable sense
of collaboration between CPU and GPU.

The LL wavefront advances by about 7 exponents per hour.
[b]ATM[/b] GPUs are great for TF alone. How many are needed to
TF the exponents in the 53M range to an extra bit or so,
thus incentivizing LL uptake, as you have done for my exponent?
10 or 20 or so.
I certainly feel morally obliged to complete this test now!
5% done.

David

[QUOTE=R.D. Silverman;264762]No, but the opposite is true. Run P-1 first. Then don't bother running TF on the bounds covered by P-1. ... we are sure there are no factors smaller than 2 B2 p + 1.[/quote]

This works but is non-optimal. With p ~2^26, B2~2^22, if we P-1 first we can skip TF to 2^49. Alas, TF to 2^49 can be done in a split second. It is much faster to do the TF to avoid the time consuming P-1.


[quote]If I were doing things, rather than run both P-1 and TF, I would simply
increase the bounds on P-1 somewhat and give up on TF. This might
miss a few factors, but I think would save time overall. One would
need to compute the probabilities for various B1/B2 and TF bounds to
determine a good choice for the bounds, as well as compare the run-times.
I am not very motivated at the moment to do such analysis. It would
make a nice undergrad level research project.[/quote]

This isn't too hard to optimize if all the work is being done on the same machine. However, we've recently had an influx of GPUs doing TF, whereas the LLs are mostly done on Intel/AMD CPUs. I don't know that you can solve for the optimal TF limits and P-1 bounds without knowing exactly how many GPUs and CPUs are active and what work type they are doing. Right now I'm stumbling around trying to find the best TF limits such that the TFers and LL testers progress at roughly the same rate.

GIMPS is weird in that the server has very limited abilities to allocate resources. GIMPS would be better served by moving much of the TF firepower over to LL testing. Since I can't do that, I do more TF than necessary to keep the over-allocated resource busy.

[quote=davieddy]Not for the first time, Bob is talking through his arse.[/quote]

Mr. Silverman is making an effort to be more civil. Please return the favor.

[QUOTE=Prime95;264790]This works but is non-optimal. With p ~2^26, B2~2^22, if we P-1 first we can skip TF to 2^49. Alas, TF to 2^49 can be done in a split second. It is much faster to do the TF to avoid the time consuming P-1.




This isn't too hard to optimize if all the work is being done on the same machine.

[/QUOTE]

The difficulty is in the analysis of the conditional probability:
Given P-1 limits of B1, and B2, and a TF factoring bound K,
what is the conditional probability of [b]finding[/b] a factor with
TF (with the given bound) given that P-1 [b]failed[/b]. If this is
sufficiently low and depending on how long it takes to run P-1 and TF
to the given bounds, it may not be worthwhile to perform TF at all.

The mathemtical difficulty here is identifying all of the conditions
under which P-1 might fail, yet still have TF succeed. I already gave
one such condition.
[QUOTE]

However, we've recently had an influx of GPUs doing TF, whereas the LLs are mostly done on Intel/AMD CPUs. I don't know that you can solve for the optimal TF limits and P-1 bounds without knowing exactly how many GPUs and CPUs are active and what work type they are doing.

[/QUOTE]


Indeed. The fact that these machines all run at different speeds makes
the optimization quite difficult.

[QUOTE=Prime95;264790]This works but is non-optimal. With p ~2^26, B2~2^22, if we P-1 first we can skip TF to 2^49. Alas, TF to 2^49 can be done in a split second.

.[/QUOTE]

I suspect that B2 ~ 2^22 is too small.

Note also that P-1 will find quite a lot of factors that would also be found
by TF.

It might be worthwhile to go through the historical data and ask:
How often did TF find a factor that would have been missed by P-1
if it were run first? How often would P-1 have succeeded in finding
a factor that was first found by TF?

[QUOTE=Prime95;264790]

Mr. Silverman is making an effort to be more civil. Please return the favor.[/QUOTE]

Indeed...Bob's reply was quite civil. He answered my question, although I think at this point we have enough empirical data that we could get a good approximation of the number of factors in a given bit range that would be found by P-1. In perfect pure math fashion, he left that to me as an exercise!

As an operator of both CPUs and GPUs, my remark is that it is 10x easier to get a GHz day of GPU credit than CPU credit on my $100 GPU...and I suspect that is 128x for some with better GPUs than mine...which translates to 7 extra bit levels for the same effort measured on the clock. That removes ~10% additional LL candidates if the initial TF level is around 70.

We need to get the GPUs doing more LL and maybe P-1....I'm currently committed to some improvements to mfaktc, but most of the time has been spent on build tools and learning Prime95 and other bits like MPQS...we need a beginner's thread for doing LL on GPUs; my choice of mfaktc is actually arbitrary, and might have been different if my GTX210 had been able to run LL.

If it was my server, I'd set the TF level to 72 or 73 bits before handing out the LL assignments, and TF exponents approaching LL assignment first. I'd re-calculate my optima by devaluing TF effort by a factor of 10-100, for the reasons stated above...and consider getting an extra bit or two of TF on stuff awaiting LL-D assignments. From my perch, it feels (with no mathematical justification) like a slightly longer view is being taken of TF, with the exponents being removed from the LL pool below 60M being the criterion for which exponents to TF how far, rather than pulling in the time of discovery of M48. This is fine with me.

Oh, and.....
:direction:

[QUOTE=R.D. Silverman;264801]
It might be worthwhile to go through the historical data and ask:
How often did TF find a factor that would have been missed by P-1
if it were run first? How often would P-1 have succeeded in finding
a factor that was first found by TF?[/QUOTE]

A very sensible and relevant question, which I et al have raised before.

Bearing in mind that all exponents from ~1M to 1000M have been TFed
to 64 bits, what, in your esteemed opinion, is your estimate?

David

[QUOTE=Prime95;264790]
Mr. Silverman is making an effort to be more civil. Please return the favor.[/QUOTE]

I did, but someone has seen fit to delete it.

Stop playing God

[QUOTE=Christenson;264803]Gone off the course.[/QUOTE]
Yes indeed. There are 91 days left until we match the longest gap in the GIMPS era. And 114 days from hitting the average gap + 2 std dev.
10metreh has our next closest (non-expired) guess, 59,278,411 on 6/30/2011
And: [QUOTE]Countdown to testing all exponents below M(43112609) once: 868[/QUOTE]makes the guesses look like a bad bet:
tom11784.....38,066,453 [strike]6/23/2007[/strike]
T.Rex...........38,500,000
PrimeCrazzy..39,999,999 [strike]9/1/2007[/strike]
wpolly..........41,991,811 [strike]4/19/2008[/strike]
lycorn..........41,999,999 [strike]11/30/2007[/strike]
Andi47.........42,000,000 [strike]8/1/2007[/strike]
edorajh........42,500,000 [strike]10/1/2009[/strike]

[QUOTE=Christenson;264803]Indeed...Bob's reply was quite civil.
Oh, and.....
:direction:[/QUOTE]

And I didn't imply otherwise.
Unfortunately a post or two has been deleted by whatever god
is currently in charge, so even less point in crying over spilt milk.

We are unanimous about moving this digression to a separate thread
(Primenet Forum the most appropriate place).
Start with my initial invitation for TF help, as UncWilly suggested.

Leave the Lounge and start talking turkey!

Suggested title:
"How can GPUs best accelerate the discovery of M48?"


David

Pot meet Kettle
 

:threadhijacked:[QUOTE=Uncwilly;264810]Yes indeed. There are 91 days left until we match the longest gap in the GIMPS era. And 114 days from hitting the average gap + 2 std dev.
10metreh has our next closest (non-expired) guess, 59,278,411 on 6/30/2011
And: makes the guesses look like a bad bet:
tom11784.....38,066,453 [strike]6/23/2007[/strike]
T.Rex...........38,500,000
PrimeCrazzy..39,999,999 [strike]9/1/2007[/strike]
wpolly..........41,991,811 [strike]4/19/2008[/strike]
lycorn..........41,999,999 [strike]11/30/2007[/strike]
Andi47.........42,000,000 [strike]8/1/2007[/strike]
edorajh........42,500,000 [strike]10/1/2009[/strike][/QUOTE]

[QUOTE=Uncwilly;264810]Yes indeed. There are 91 days left until we match the longest gap in the GIMPS era. And 114 days from hitting the average gap + 2 std dev.
10metreh has our next closest (non-expired) guess, 59,278,411 on 6/30/2011
And: makes the guesses look like a bad bet:
tom11784.....38,066,453 [strike]6/23/2007[/strike]
T.Rex...........38,500,000
PrimeCrazzy..39,999,999 [strike]9/1/2007[/strike]
wpolly..........41,991,811 [strike]4/19/2008[/strike]
lycorn..........41,999,999 [strike]11/30/2007[/strike]
Andi47.........42,000,000 [strike]8/1/2007[/strike]
edorajh........42,500,000 [strike]10/1/2009[/strike][/QUOTE]

At 868 not LL'ed once under [SIZE=2]M(43,112,609[/SIZE]), it is starting to look like the long, heavy tail under M(24,[SIZE=2]036,583)[/SIZE]. I think it's time to add
Countdown to All exponents under 50M LL'ed once
and
Countdown to All exponents under 60M LL'ed once
to the milestones page. Maybe also consider 50th percentile (just as many exponents not LL'ed below this point as are LL'ed above this point) LL point to the list.

Mentioning that we've gotten off track in a second direction was intended as an off-hand remark, a dry observation of the state of affairs to which I certainly contributed. And I'm OK with moving this digression to a thread of its own....

My bet: M48 =M(~55M)...date? 11/11/11.....

[QUOTE=davieddy;264808]I did, but someone has seen fit to delete it.

Stop playing God[/QUOTE]

Disagree with Bob's analysis all you like, but please do so without calling him or anyone else an arse or a 2-year-old. I understand you and Bob have a rather unpleasant history. Let it go.

And believe me, I do have better things to do with my time than playing God.

[QUOTE=davieddy;264811]
Leave the Lounge and start talking turkey!

Suggested title:
"How can GPUs best accelerate the discovery of M48?"

David[/QUOTE]
I, if personally in charge of the forum, probably would have leftt your posts, not knowing the ancient history...but be glad they are gone, unavailable for anyone else to discover your silliness....you were in a touchy mood, from the first time someone pointed out the change in thread direction.

Now, as for turkey, I hope P95 doesn't mind: I don't care if it *IS* in the lounge...... here's my technical analysis:
1) Fact: GPUs accelerating TF by factor of 128 = 7 bit levels =~10% fewer LLs. AND this takes away CPU cycles that could be doing LL, so it's not quite even this good.
Opinion: We need to finish mfaktc. That means
a) automating the assignment/reporting process
b) moving the sieving onto the GPU proper, so an old CPU can run a new GPU.

Opinion: We are being overwhelmed by TF capability at the moment.
Opinionated consequence: When the current wavefront reaches 70M (or maybe sooner) it's time to do more TF on anything that hasn't had an LL-D started on it in lower ranges. A few more of these will be knocked out with known factor results.

Opinion: The increase in TF power is relatively unimportant compared to other improvements. P95 isn't thinking about AVX instructions; he needs many Giga-Neuron Days to get that going, and, although almost invisible, it will make a more significant change in the rate at which exponents are proven composite.

Opinion: Putting P-1 on GPUs is moderately important.

Opinion: Maximising GPU usage on LL tests is the single most important upgrade, as it reduces the calendar/power cost of LL testing directly. I don't think you (davieddy) can contribute to the code technically, but you can contribute, as Rodrigo has committed to, by making the path easy for others that follow you in running the code by keeping a SHORT thread with the directions. Look up "putting it all together". Hopefully P95 has made that a sticky.

In a larger sense, this is what P95 has done with Primenet...

In the meantime, I keep hunting in various ways.....and am working on the technical part of mfaktc...

Babies out with the bathwater
 

[QUOTE=Prime95;264818]Disagree with Bob's analysis all you like, but please do so without calling him or anyone else an arse or a 2-year-old. I understand you and Bob have a rather unpleasant history. Let it go.

And believe me, I do have better things to do with my time than playing God.[/QUOTE]

Sorry George, but it's impossible to attempt to defend my posts once
someone (I presume you) has deleted them.

BUT:
I did not call him an arse. I said he he was talking thereoutof.
I did not call him a 2 year-old. I said a 2 year-old could see why
he was so way off the mark re optimizing TF/P-1.

The "baby" you flushed down the toilet was my simple observation
that a handful of GPUs could TF a few more levels, while comfortably
keeping pace with the LL wavefront.
Since programming GPUs is "work in progress", no need to think further
than exponents < 60M ATM.

Maybe subtlety of meaning/tone/humour gets lost while crossing the pond.
Especially westwards:smile:

David

[QUOTE=davieddy;264827]BUT:
I did not call him an arse. I said he he was talking thereoutof.
I did not call him a 2 year-old. I said a 2 year-old could see why
he was so way off the mark [/QUOTE]

You are correct in the characterization of your previous posts. I overstepped in my description of your deleted posts (some by me, some by another moderator). Nevertheless, these posts seem needlessly incendiary considering the past tensions between the two of you.

The moderators are merely trying to nip any flame wars in the bud. They were annoying to the combatants, the readers, and the moderators. Thanks for cooperating.

[QUOTE=Christenson;264826]I, if personally in charge of the forum, probably would have leftt your posts, not knowing the ancient history...but be glad they are gone, unavailable for anyone else to discover your silliness....you were in a touchy mood, from the first time someone pointed out the change in thread direction.

1) Fact: GPUs accelerating TF by factor of 128 = 7 bit levels =~10% fewer LLs. AND this takes away CPU cycles that could be doing LL, so it's not quite even this good.
......

I don't think you (davieddy) can contribute to the code technically, but you can contribute...[/QUOTE]

Cheers Christenson:smile:

David

PS remove your tongue from Bob's ****.

[QUOTE=Christenson;264816]My bet: M48 =M(~55M)...date? 11/11/11.....[/QUOTE]I have added it to my list.

Live by the sword...
 

[QUOTE=Prime95;264828]You are correct in the characterization of your previous posts. I overstepped in my description of your deleted posts (some by me, some by another moderator). Nevertheless, these posts seem needlessly incendiary considering the past tensions between the two of you.

The moderators are merely trying to nip any flame wars in the bud. They were annoying to the combatants, the readers, and the moderators. Thanks for cooperating.[/QUOTE]

I realise that if you use sarcasm/parody frequently, the
casual reader may not know whether you are joking or not.

When I referred to your "usual tact", I certainly meant it. Really.

I appreciate that Mod works in mysterious ways:smile:

David

Lighten the mood
 

[QUOTE=Uncwilly;264830]I have added it to my list.[/QUOTE]
[url=http://www.youtube.com/watch?v=A45xqLHccRo]I've Got a Little List[/url]
David

[QUOTE=Prime95;264790]GIMPS would be better served by moving much of the TF firepower over to LL testing. Since I can't do that...[/QUOTE]

Why not? How about temporarily eliminating/limiting TF (below 100M) as an available worktype, and handing out DCs or LLs (or if we must, for those who really, really want to TF, TF-LMH assignments) instead?

[QUOTE=NBtarheel_33;264839]Why not? How about temporarily eliminating/limiting TF (below 100M) as an available worktype, and handing out DCs or LLs (or if we must, for those who really, really want to TF, TF-LMH assignments) instead?[/QUOTE]

"Find out what little Johnnie is doing and tell him to stop it".
(He is using his GPU to do what it does best ATM).

There are two different motives for TF.
One is to find factors as frequently as possible.
The other is slightly more subtle: eliminate the necessity for two LL tests,
(in a few cases) and enhance the chance of the rest being prime.

The latter is what we are discussing, and may be viewed as a thankless
task: little reward (factors) for much* time. I have assured Christenson that if the number I am currently testing turns out to be prime, I shall
publicly acknowledge his TFing 6 more levels, thereby ensuring my "effort"
was worthwhile, and donate an appropriate number of $ should I win any!

* "much" here means about a day on his GPU, which has to be compared
with 2 months for the LLtest on my CPU.
There was a 9% chance of him finding a factor, thereby
sparing me a futile LLtest.

David

Deleting thoughts
 

[QUOTE=davieddy;264827]
The "baby" you flushed down the toilet....[/QUOTE]

Another one was this:
Look at the size of the typical factor found via P-1 compared with
the TF max to judge how little the two enterprizes overlap each other.

David

[QUOTE=NBtarheel_33;264839]Why not? How about temporarily eliminating/limiting TF (below 100M) as an available worktype, and handing out DCs or LLs (or if we must, for those who really, really want to TF, TF-LMH assignments) instead?[/QUOTE]

That would be fine, but right now, the firepower, as a group, and this includes myself, goes to the "manual assignments" page, and says: Gimme a TF assignment (or a hundred or three)...and then proceeds to TF it in a jiffy with a hot GPU. It will get a bit worse when mfaktc is upgraded to automatic mode, as the program will do this for us on automatic, so very little neurological bandwidth will be required. Thus it is I suggest P95 increase the TF bit levels, even on exponents that have already received a first LL.

There isn't a way to say "Give me the assignment that makes the most sense for GIMPS"...there is no CUDA P-1 program, and I don't have the CUDA LL program installed....although maybe I should. Thus it is I encourage DavieDDy to make that task easier.

P-1 on my CPUs has actually been significantly more productive in eliminating LL candidates than running LL tests.

[QUOTE=Uncwilly;264810]Yes indeed. There are 91 days left until we match the longest gap in the GIMPS era. And 114 days from hitting the average gap + 2 std dev.
10metreh has our next closest (non-expired) guess, 59,278,411 on 6/30/2011
And: makes the guesses look like a bad bet:
tom11784.....38,066,453 [strike]6/23/2007[/strike]
T.Rex...........38,500,000
PrimeCrazzy..39,999,999 [strike]9/1/2007[/strike]
wpolly..........41,991,811 [strike]4/19/2008[/strike]
lycorn..........41,999,999 [strike]11/30/2007[/strike]
Andi47.........42,000,000 [strike]8/1/2007[/strike]
edorajh........42,500,000 [strike]10/1/2009[/strike][/QUOTE]

Have you googled "Gambler's Phallusy" yet?

If so, why do you persist with this puerile poop?

Tried to get the "smily" but it was taking forever for the
page to come up. Laxative required.
I bet you are partly to blame.

David

[QUOTE=davieddy;264842]Another one was this:
Look at the size of the typical factor found via P-1 compared with
the TF max to judge how little the two enterprizes overlap each other.

David[/QUOTE]

And you somehow think that this is a mathematical argument???

All you have done is gainsay the mathematics that I have presented,
claiming that my arguments were "pulled from my ass" or "bull".
What a mature way to conduct a technical discussion.

Did it ever occur to you that P-1 is generally a better algorithm?
That it is expected to find larger factors on average? Do you
understand why?


Did it occur to you that TF is usually done first, and its factors
are bounded in size? Try running P-1 [b]first[/b] and you will find that
many/most of the factors found by TF will now be found by P-1.
You will also find that the variance of the size of factors found by
P-1 will increase.

I am suggesting that you can SAVE TIME by NOT running TF at all;
Just run P-1 with slightly higher bounds that are currently used.

[QUOTE=Prime95;264828]You are correct in the characterization of your previous posts. I overstepped in my description of your deleted posts (some by me, some by another moderator). Nevertheless, these posts seem needlessly incendiary considering the past tensions between the two of you.

The moderators are merely trying to nip any flame wars in the bud. They were annoying to the combatants, the readers, and the moderators. Thanks for cooperating.[/QUOTE]

He also failed to discuss any mathematics! All he did was claim that
my arguments were bull; a reflection of his mathematical ignorance.

Claiming that a 2 yr old would see that my arguments were wrong
without bothering to even discuss the mathematics [b]IS[/b] a form
of derision.