[QUOTE=xilman;381382]Bob, I will also ask you to tone it down.

There's a phrase you often use which concerns assuming facts no in evidence. There's a phrase I often use which contains the words "malice" and "incompetence".

I see absolutely no evidence whatsoever from the postings made so far that alpertron was being maliciously provocative.

If you (that is, both of you) wish to take this particular dispute further, please move it to PM. I would appreciate being copied on the discussion but that's your decision.

Paul[/QUOTE]

I have instead taken jason's advice: Since my comments throughout this
thread have been repeatedly ignored and since my comments are obviously
not valued, I withdraw from future comments and also place alpertron
and pdazzl on my 'ignore; they do not listen and are unteachable' list.

BTW, in response to the strong urge that the moderators seem to have to
practice censorship, I point to Voltaire:

[url]http://www.brainyquote.com/quotes/quotes/v/voltaire109645.html[/url]

The moderators, it seems, do not defend people's right to "say it".

[QUOTE=R.D. Silverman;381383]BTW, in response to the strong urge that the moderators seem to have to practice censorship, I point to Voltaire:

[url]http://www.brainyquote.com/quotes/quotes/v/voltaire109645.html[/url]

The moderators, it seems, do not defend people's right to "say it".[/QUOTE]Once more, assuming facts not in evidence. You have been asked to tone down your rhetorical style. I have seen no evidence whatsoever that you have been prevented from presenting your views in a calm and reasoned manner. I have specifically stated that you may continue your discussion, have suggested a medium through which it may be conducted, and have requested that I be party to that discussion.

OK, enough from me on this particular spat. We can continue in the Soapbox if you would like a larger audience than PM allows. It's clear that this is no longer about mathematics and does not belong here.



Paul

[QUOTE=R.D. Silverman;381383]I have instead taken jason's advice: Since my comments throughout this
thread have been repeatedly ignored and since my comments are obviously
not valued, I withdraw from future comments and also place alpertron
and pdazzl on my 'ignore; they do not listen and are unteachable' list.

BTW, in response to the strong urge that the moderators seem to have to
practice censorship, I point to Voltaire:

[url]http://www.brainyquote.com/quotes/quotes/v/voltaire109645.html[/url]

The moderators, it seems, do not defend people's right to "say it".[/QUOTE]

Sorry to hear; perhaps I'm speaking for the majority: you obviously have a great deal of knowledge which is welcomed....it's just the name calling and vulgar language isn't. The whole point of starting this thread is so experts like yourself can add guidance to us excel users in the peanut gallery. If we don't heed your advise that's our choice. Anyways wish you well, onwards and upwards.

I concur with the previous poster.

I was reading some proofs of Erdos-Kac theorem. It appears that it does not work "as expected" in our case because the product of all known prime factors have less than 500 digits, which is less than 0.01% of the size of the number.

In this case, the extremely small primes (when compared to the Mersenne number) are essentially independent. Thus the presence of a new prime factor does not depend on the presence of other prime factors. So wblipp's numbers appear to be OK.

[QUOTE=alpertron;381379]Notice that [url]http://www.mersenne.ca/manyfactors.php[/url] does not show results if the number of known prime factors is less than 4, so all those examples with StopAfterFactor=1 are automatically discarded.
[/QUOTE]
They are discarded, so the distribution [I]is[/I] skewed.
The fairly arbitrarily picked "candidates" were disproportionately sieved, and the distribution is skewed again.

Try [URL="http://www.mersenne.ca/exponent/3396244391"]M3396244391[/URL]. Does it have 2 prime factors... or >8? [SPOILER]It does have more than eight. Try it.[/SPOILER]

[QUOTE=pdazzl;381385]Sorry to hear; perhaps I'm speaking for the majority: you obviously have a great deal of knowledge which is welcomed....it's just the name calling and vulgar language isn't. The whole point of starting this thread is so experts like yourself can add guidance to us excel users in the peanut gallery. If we don't heed your advise that's our choice. Anyways wish you well, onwards and upwards.[/QUOTE]

I agree with this, too.

[QUOTE=alpertron;381356]So the probability to find the prime factor is not very small as other people said before in this thread.[/QUOTE]

Admittedly, I chortled when I read this statement although I disagreed with the name-calling.

In fact, I would normally not admit to "laughing" at the ignorance in this statement. The reason I do is just to show that I see that it's obviously wrong, but that there is a better way of dealing with it.


Just because an event occurs, this does not mean that the event is necessarily likely to occur.

Grab a coin, and flip it twenty times, logging the result, in order. I will do that myself, right now:

H T H T H T H H H T T H H H H T T T T H

Now, consider that the odds of getting that exact sequence of heads and tails is 2[SUP]20[/SUP], one power of two per toss. 1 chance in 1048576, specifically. It happened, even though the odds are 1 in a million.


In the same way, the odds of finding an eleventh factor (and proving the existence of thirteen) weren't very high, but that in no way prevents this event from occurring.

However, this COULD be the first of a number of events which bring into question the integrity of the prediction. One time, not likely, but possible. If we randomly pick another exponent with 9 factors and find two or three more, that is VERY not likely, but possible. If we pick a third, and AGAIN find factors despite the prediction that we won't, we can start to ask ourselves if the prediction is actually any good.

I don't really understand how we can "prove" anything about the behaviour of such random things as prime numbers and the distribution of factors in a number, but I'll take it for granted that the conjectures are "close enough" for now.

[QUOTE=Batalov;381392]They are discarded, so the distribution [I]is[/I] skewed.
The fairly arbitrarily picked "candidates" were disproportionately sieved, and the distribution is skewed again.

Try [URL="http://www.mersenne.ca/exponent/3396244391"]M3396244391[/URL]. Does it have 2 prime factors... or >8? [SPOILER]It does have more than eight. Try it.[/SPOILER][/QUOTE]
Yes, I said that the table on mersenne.ca is incomplete, but the idea was not to have quantitative results (which require that the table be complete and this would require several millenia-CPU) but qualitative results.

According to Bob, if a Mersenne number already has several known prime factors, the probability of having more factors is extremely remote, and more remote as we know more factors. So I do not see how we know 11 prime factors of some Mersenne number if that is true, and several Mersenne numbers with 8, 9 and 10 prime factors. That's why I said that something was wrong with respect to probabilities.

[QUOTE=TheMawn;381393]
[...]
In the same way, the odds of finding an eleventh factor (and proving the existence of thirteen) weren't very high, but that in no way prevents this event from occurring.
[...]
[/QUOTE]
Suppose the probability of finding a new prime factor if more than 6 primes are known is 1 in 100 (not extremely remote).

Then, in order to find the 7th factor we would have 1 chance in 100. That would be possible, because we have lots of Mersenne numbers to check.

But then we find the 8th, 9th, 10th and now the 11th. That's 1 chance in 10,000,000,000. We can start to have some doubts about the statistics, but we can also have good luck.

But then you can find other Mersenne numbers with 10 prime factors. That's one chance in 100,000,000 and several Mersenne numbers with 9 prime factors. That's 1 chance in 1,000,000 for each hit.

It is clear that far from good luck, something wrong occurs with the probabilities.

[QUOTE=Batalov;381392]They are discarded, so the distribution [I]is[/I] skewed.
The fairly arbitrarily picked "candidates" were disproportionately sieved, and the distribution is skewed again.

Try [URL="http://www.mersenne.ca/exponent/3396244391"]M3396244391[/URL]. Does it have 2 prime factors... or >8? [SPOILER]It does have more than eight. Try it.[/SPOILER][/QUOTE]

Nice find

[URL="http://www.mersenne.ca/exponent/3273488573"]M3273488573[/URL] has 9 (and >=1 invisible one). It is rather easy to find them.