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Old 2007-10-09, 06:16   #210
Mr. P-1
 
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Quote:
Originally Posted by jasong View Post
If his method works, it's another possible way to figure out the distribution of Mersenne numbers. It's very possible that's it both a combination of random chance and special rules involving these numbers. Maybe at these high numbers, all the unknown special rules coalesce into something very much resembling an independent pattern.
If..., possible..., possible..., maybe...

The problem is that you can [i]always[i] find an a pattern which retrofits known data, even completely random data, especially if it only has to fit "the last few primes". In other words, if you disregard all the data that it doesn't fit.

So the existence of such a retrofitted pattern tells us nothing.

Now if there were genuine mathematical theory behind his spreadsheet then it would be a different matter. But as he's shown himself to be incapable of testing seven-digit exponents for primality, it's unlikely, as I said, that he could succeed where mathematicians have failed.
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Old 2007-10-09, 20:03   #211
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Quote:
Originally Posted by Mr. P-1 View Post
If..., possible..., possible..., maybe...

The problem is that you can [i]always[i] find an a pattern which retrofits known data, even completely random data, especially if it only has to fit "the last few primes". In other words, if you disregard all the data that it doesn't fit.
Yes, that's why it's called a heuristic rather than a theory. Classical mechanics works for most of the things we deal with, but when you're dealing with an extreme amount of mass or sub-light speeds, it falls apart.
Quote:
Now if there were genuine mathematical theory behind his spreadsheet then it would be a different matter. But as he's shown himself to be incapable of testing seven-digit exponents for primality, it's unlikely, as I said, that he could succeed where mathematicians have failed.
All theories start out as hypotheses, and the ones that go into new territory usually only tell half the story. It's possible to be a fantastic cook without realizing that the boiled water goes somewhere else as steam
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Old 2007-10-10, 12:43   #212
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Yes, that's why it's called a heuristic rather than a theory.
I didn't refer to "a" theory. The words "theory" and "hypothesis" have different meanings in mathematics from the empirical sciences. In mathematics, "theory" refers to a body of related mathematical knowledge - number theory, group theory, category theory, etc., while "hypothesis" seems to be more or less synonymous with "conjecture" - Riemann hypothesis, continuum hypothesis, etc, i.e., a statement for which there is strong evidence, short of mathematical evidence, that it is true.

A heuristic argument in mathematics is one which is based upon reasonable but unproven assumptions about the statistical properties of the objects under consideration, in this case, Mersenne primes. Thus far, neither you nor cochet have been able to articulate a valid heuristic argument in support of his spreadsheet.

In short, you have nothing.

Quote:
Classical mechanics works for most of the things we deal with, but when you're dealing with an extreme amount of mass or sub-light speeds, it falls apart.
I presume that by "Classical mechanics" you mean Newtonian mechanics. Yes it fails to predict the behaviour of matter at high speeds under extreme gravitational fields. Its replacements - Special and General Relativity - work in these extreme cases.

But SR and GR also work in the mundane arena where Newton works. In fact SR and GR reduce to Newton in the limiting case. Does cochet's method have these virtues? Can it explain the linearity of the graph at the top of this page? For which extreme cases does Wagstaff's conjecture break down? You already said that cochet's only works for the last few Mersenne Primes. Wagstaff's works for them all.

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All theories start out as hypotheses, and the ones that go into new territory usually only tell half the story.
Theories do not start out as patterns seen in the clouds.
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Old 2007-10-11, 02:10   #213
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Mr. P-1, theories can start anywhere, even as patterns seen in clouds. Perhaps you meant that in order to be valid or useful, there has to be more to a theory than mere cloud patterns.

jasong, theories that cannot pass the test of predictive reality are cheaper than "a dime a dozen" and as plentiful and valuable as pebbles. I myself have had several inspirations for a theory to predict Mersenne primes. So far, every one has failed the test of realistic prediction, as has the one presented by cochet. The value of a theory is determined by its predictive success, not anyone's wishful thinking.
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Old 2007-10-11, 02:46   #214
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Quote:
Originally Posted by Mr. P-1 View Post
Thus far, neither you nor cochet have been able to articulate a valid heuristic argument in support of his spreadsheet.

In short, you have nothing.
Obviously, you haven't even looked at the spreadsheet and are simply trying to piss me off, I had my doubts until now.
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Old 2007-10-11, 06:31   #215
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Obviously, you haven't even looked at the spreadsheet and are simply trying to piss me off, I had my doubts until now.
I hadn't looked at it. I tried to download it when he first posted the URL and got an error. Ditto his webpage.

I've downloaded the spreadsheet now. (The webpage is still 404 compliant.)

Starting with the known Mersenne primes he calculates repeated backward absolute differences. He then calculates the ratio between successive values of the penultimate difference and observes, golly gosh, that some are close to 1 and some aren't. On the basis of this he predicts that the next one will be 1, or close to it. Specifically he thinks AV18 in his sheet should be 13399. He's found an exponent which yields this values, and bingo: that's his prediction.

Question: How many different exponents will give this value? Hint: AV19 doesn't have to be zero. It could be 26798. In general, each value in the column has two potential predecessors.

Question: How many different exponents will give close to this value? How close is close?

Question: What is the probability that random data will yield ratios between successive penultimate differences close to 1?

As an experiment, I wrote a script to randomly generate a set of prime exponents distributed according to Wagstaff's heuristic. I plugged these faux Mersennes into Cochet's spreadsheet and guess what happened? Some of the ratios are close to 1 and some aren't. Wow! Do you think I could use his spreadsheet to predict the next number in a random sequence?

Some people actually believe they can do that. Some people think that by staring hard enough at the roulette wheel and seeing patterns in the clouds they can predict the next winner. Strangely, the casinos all remain in business.

Oh yeah, and there's that alternating pattern. The last eight ratios (count them) alternate between being close to 1 and not close to 1. That's like watching forty plays on a roulette wheel, noticing that the last eight went red, black, red, black, red, black, red, black, and predicting that the next will be red.

It's a pattern in the clouds. You still have nothing.

I'm sorry if it pisses you off to be told that. It's not my intention to piss you off, but you still have nothing, whether it pisses you off or not.
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Old 2007-10-11, 06:38   #216
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And on the subject of alternating patterns, what are the next two numbers in the following sequence:

2, 7, 1, 8, 2, 8, 1, 8, 2, 8, ...
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Old 2007-10-11, 13:09   #217
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Quote:
Originally Posted by Mr. P-1 View Post
And on the subject of alternating patterns, what are the next two numbers in the following sequence:

2, 7, 1, 8, 2, 8, 1, 8, 2, 8, ...
45, 90, 45

See, it still alternates!


Paul

Last fiddled with by xilman on 2007-10-11 at 19:29 Reason: Changes "repeats" into "alternates"
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Old 2007-10-11, 18:10   #218
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Good, Mister M-1, you have realized a decisive step : you have finally taken knowledge of the spreadsheet, you have read it. Excellent. Itโ€™s to say that before, you were into an โ€œa prioriโ€ about the question, and you were victim of a โ€œready-madeโ€ idea.
Now, it become possible to discuss a minimum.
But you have to jump a new step (number 2) : simply read what I said in my attached pages. You donโ€™t have do that.

I donโ€™t know what you are saying about "some values closed to 1 and others that are'nt" ; itโ€™s not the base of my argumentation (itโ€™s possible you have found that on the sheet, but these are secondary calculus). No, the interesting question you ask concerns the status of the number 13399 in AV18. I have two remarks about it :
1) this number and the followings at the top of the 45ft column are the most plausible considering the laws given in one of my posts (haut colonne.html)

2) itโ€™s evident that this number in AV18 correspond at a large number of exponents at the bottom of the column. But, this is already a progress : all the exponents do not go to this number (we can eliminate some of these).
But more, if you read what I said, we need the application of some rules at the bottom of the column, to delimitate brackets more and more reduce. The Rรจgle IV is one of these.
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Old 2007-10-11, 20:04   #219
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lol, I thought you'd left cochet.

Have you been lurking about all this time and just not saying anything? Just wondering.
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Old 2007-10-11, 21:05   #220
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I'am always alive !
But I must precise that the only argument that would refute my these would be that any random suite of odd numbers presents ("donne lieu ร ") the sames rules into the grid of their differences in absolute value. I think all the same at a specificity of the mersenne suite, on the model of the prime suite's grid studied by Proth and Gilbreath (with the production of their conjecture).
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