[QUOTE=xilman;106652]Roger Needham used to describe serendipity as searching for a needle in a haystack and finding the farmer's daughter![/QUOTE]

I'm really tempted to make a "What's the difference between finding a needle in a haystack and finding the farmer's daughter there? The one pricks your finger..." joke at this juncture --

But that would be beneath me.

[QUOTE=ewmayer;106653]I'm really tempted to make a "What's the difference between finding a needle in a haystack and finding the farmer's daughter there? The one pricks your finger..." joke at this juncture --

But that would be beneath me.[/QUOTE]

I thought it was the farmer's daughter that were beneath you :lol:

-Eivind

[QUOTE=Eivind;106693]I thought it was the farmer's daughter that were beneath you :lol:[/QUOTE]

I don't deny the possibility ... but I don't like to kiss and tell. (But let's just say that I'm lazy, so the opposite is at least equally likely. If the FD wants to do most of the work, then by all means let her, I say. I'm all for greater involvement of women in the workplace ... yes, that's it, it not's that I'm lazy, it's just that I'm such a social progressive... ;)

[quote=cochet;106181]You can consult the famous method (for some hours) at this address :
[URL]http://home.tele2.fr/lacanmaths/peremersenne.html[/URL]
[/quote]
I'm sorry I was not following this thread at the right moment to have an idea about that method. Too bad.
Can anyone find it still in your browsers history (& cache) ?
Anyway, I think my post from 26 Mar 07, 08:13 PM
still expresses best what one should think of that method:
it is not at all efficient to eliminate enough candidates.
I suppose trial factoring to 32 bits is more efficient.

In some sense, I'd like to see your method/procedure just to give you a counter-example or to tell you where it is wrong.
So it's your choice, Cochet, if you want some help.

I just remind you that you do not have any proof (the proof of this statement is given by all numbers you gave so far which were wrong, now you put a "bracket" 37oooooo-372ooooo which is just less easily refutable - I mean it just takes longer, since there are 2oo ooo exponents in that range (and even if there are a factor log(...) less primes...)

The best to guarantee your intellectual ownership is to publish your method, and since it will never be accepted in a journal (I'm sorry but this is an evidence, independent of whether your method is right or wrong),
a good place to do it would be here.

PS: it's not surpring that all your proposals are undergoing LL tests at present since the bracket you gave is just beneath GIMPS "wave front", and you avoid now putting non-primes and primes which are in factor.txt.

[QUOTE=m_f_h;107515]In some sense, I'd like to see your method/procedure just to give you a counter-example or to tell you where it is wrong.[/QUOTE]

Given that fully 8 of the first 11 of cochet's "predictions" are known composites (3 still being tested), how many more examples do you need?

Oh, wait -- I'll bet the miraculous *method* is correct, he's just implementing it wrong ... yeah, that's the ticket...

[QUOTE=Xyzzy;99851]BTW, our wealth of ignorance of the French language would astound you.[/QUOTE]
Speak for [i]vourself[/i], mon ami. I am not at all astounded by my ignorance of French.

[QUOTE=Flatlander;99875]My wife said to me "Je t'adore!" so I told her to shut it herself.[/QUOTE]
Completely missed this [i]bon mot[/i][sup]*[/sup] on my first read-through - very nice, Monsieur des Plaines!

-----------
[sup]*[/sup]BTW, that's French for "lovely witticism"

[QUOTE=T.Rex;102131]Thanks. However, this figure (plus explainations) already is available at this Caldwell Primes' [URL="http://primes.utm.edu/notes/faq/NextMersenne.html"]page[/URL].
T.[/QUOTE]

Doesn't this imply that a statement could be made that goes something like this?

"There is a 95% level of confidence that M45 should be found before candidate Mxxxxxxxx (insert number probably around 40 something million).

If that is the case, has anyone reasonably made that statement?

Then we could determine based on how much processing power is available when it is likely that M45 will be found by (NB: not found, but found by).

Rob.

[QUOTE=rgiltrap;107879]Doesn't this imply that a statement could be made that goes something like this?
"There is a 95% level of confidence that M45 should be found before candidate Mxxxxxxxx (insert number probably around 40 something million)."[/QUOTE]I think that the answer is: yes. On Caldwell's page, the 2 last figures of paragraph "What about the next Mersenne?" do not seem updated with M45. I do not understand the sentence: "Cumulative probability that t (...) occurs by" related to 100% probability when abscisse is 27.5 . What means 27.5 ???
T.

[quote=T.Rex;107880]I do not understand the sentence: "Cumulative probability that t (...) occurs by" related to 100% probability when abscisse is 27.5 . What means 27.5 ???[/quote]27.5 is just where Caldwell chose to end the graph. At that abscissa [I][Hey! This is great! I haven't used either "abscissa" or "ordinate" in a sentence for a long time.][/I] the probability is still below 1.00 (or just above 0.00 on the graph above that), but the gap doesn't show well at that scale, which is probably why Caldwell ended the graph there.

[QUOTE=cheesehead;107909]27.5 is just where Caldwell chose to end the graph. [/QUOTE]OK.. But what means these numbers ? Exponents of Mersenne numbers ? That would mean that the probability to find M45 is near 100 % since exponent 27.5 ? (some years ago !) Sorry, it still does not make sense for me (or the figures of Caldwell are not up to date with his text).
T.

[quote=T.Rex;107923]OK.. But what means these numbers ? Exponents of Mersenne numbers ?[/quote](Oh, [i]now[/i] I see the difficulty.)

No, the abscissas that go from 24.5 to 27.5 (and 10.0 to 40.0) in his section "What about the next Mersenne?" are all log[sub]2[/sub](log[sub]2[/sub](M[sub]n[/sub])).

I think you've been misled by a graphing inconsistency on that page.

At page top, Caldwell's first graph on the page has log[sub]2[/sub](log[sub]2[/sub](M[sub]n[/sub])) plotted as the [U]ordinate[/U] versus n as abscissa. But later, in his section "What about the next Mersenne?", he plots log[sub]2[/sub](log[sub]2[/sub](M[sub]n[/sub])) as the [U]abscissa[/U] each time. Perhaps that inconsistency has obscured his intent.

[quote](or the figures of Caldwell are not up to date with his text).[/quote]He has updated some, but not all, of his page to reflect discovery of the 44th Mersenne. Some "43"s need to be changed to "44" in his "What about the next Mersenne?" section.

I'll send Prof. Caldwell a note.

[quote=rgiltrap;107879]Doesn't this imply that a statement could be made that goes something like this?

"There is a 95% level of confidence that M45 should be found before candidate Mxxxxxxxx (insert number probably around 40 something million).

Rob.[/quote]

According to the GIMPS status page, the expected number of primes
before exponent 79,300,000 is 2.08.
That gives a probability of 12.5% that no prime will be found before then.
Your requested confidence level is too high to be useful.

There is a 72% probability that M45 will be higher than 40,250,000,
and a 41% probability it will be higher than 50,000,000.