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....