M7508981 has at least 12 prime factors(new factor # record)

[jasonp]

Bob: tone it down. AGAIN.

[R.D. Silverman]

Originally Posted by jasonp

Bob: tone it down. AGAIN.

I will when people who have not studied this subject stop contradicting
me. Alpertron made one of the more idiotic statements that I have
seen in a long time. It amounted to:

A rare event occurred. Therefore the probability that it occurred was
not that high. He then repeated it.

Classic gambler's fallacy.

[alpertron]

Originally Posted by R.D. Silverman

I will when people who have not studied this subject stop contradicting
me. Alpertron made one of the more idiotic statements that I have
seen in a long time. It amounted to:

A rare event occurred. Therefore the probability that it occurred was
not that high. He then repeated it.

Classic gambler's fallacy.

This is not a rare event. You said that the probability was very remote. I also showed (incomplete) data, the current statistics from the known factors of Mersenne numbers, that indicated that this is not the case.

[jasonp]

I don't care what statements he made. The only name-calling in this thread is from you. The only abuse in the previous thread I had to jump into was from you. You can be civil or you can be gone.

If you feel your contribution is not being valued, just drop the matter.

[alpertron]

Originally Posted by jasonp

I don't care what statements he made. The only name-calling in this thread is from you. The only abuse in the previous thread I had to jump into was from you. You can be civil or you can be gone.

In particular I have no problem with his "extra words". But I'm interested on mathematical exchange of ideas, even though I'm not a mathematician. I still want his explanation to an earlier post of mine:

Originally Posted by alpertron

OK. Let me rephrase my thinking differently. Suppose that we know not 10 but 9 prime factors of M7508981. The probability of finding the tenth prime factor would be so extremely tiny according to Bob that it would be nearly impossible that we found the 10th prime factor.

Then we can continue backtracking, and finally we should conclude that it would be impossible with the current bounds to find more, than say 5 prime factors. This is not what occurs according to my previous post.

So it appears that something in Bob's argument is not entirely correct.

[pdazzl]

Originally Posted by R.D. Silverman

How did you reach this conclusion???`

I will give a hint: "The experts who have a better idea" have already told
you the approach to take.

And, of course, you failed to take it.

I will give two hints, just one final time.

(1) Given a factor x of a much larger number y, answer the following question:

What is the expected size of the next factor?

(2) The likelihood that continued ECM or P-1 or TF will find another factor
is very remote.

So is #2 still a credible statement as we search for factor #12 on this number? Can someone give us the odds of finding another as we currently stand?

I'd be interested to hear from wblipp what the expected median is of the next factor.

In the meantime I'm pressing on with ecm on a couple machines from 25-35 digit range.

[Batalov]

Drawing statistics from biased sets is a very unrewarding business.
(Goes without saying that one has to know statistics, first.)

I'll give you an example of the visible structure in this dataset. (Here, "structure" is the antonym of randomness; you cannot use most of the approximations when there's no randomness and i.i.d. premise is violated)

Observe http://www.mersenne.ca/exponent/630486799 . What can you learn by observation? Here is what. It is an example of how mfaktc was run en masse with default parameters. The default parameters include StopAfterFactor=1. Therefore, this is just one of a huge amount of candidates that was reported to have been run to a certain initial level... but wasn't. Factoring stopped after one or a few small factors and the rest of the tiny factors was found only at a rather ridiculous level of 80-81 bits. There is a huge amount of candidates that have unreported factors at the reported bit level. You can easily check this premise.

=> The statistics drawn from this set will be severely flawed unless a sophisticated model is built and fitted. I wholeheartedly recommend the home-grown statisticians (armed with Excel and four basic arithmetic operations) to stop plotting number towers and drawing barcharts and then kowtowing to them.

[R.D. Silverman]

Originally Posted by jasonp

I don't care what statements he made. The only name-calling in this thread is from you. The only abuse in the previous thread I had to jump into was from you. You can be civil or you can be gone.

Indeed. Being stupidly argumentative (from ignorance) with someone who
knows a lot more than you is equally offensive and disrespectful.

Or maybe you argued with your teachers when you were younger?

His remarks were made in order to be provocative. That too is offensive.

[alpertron]

Originally Posted by Batalov

Drawing statistics from biased sets is a very unrewarding business.
(Goes without saying that one has to know statistics, first.)

I'll give you an example of the visible structure in this dataset. (Here, "structure" is the antonym of randomness; you cannot use most of the approximations when there's no randomness and i.i.d. premise is violated)

Observe http://www.mersenne.ca/exponent/630486799 . What can you learn by observation? Here is what. It is an example of how mfaktc was run en masse with default parameters. The default parameters include StopAfterFactor=1. Therefore, this is just one of a huge amount of candidates that was reported to have been run to a certain initial level... but wasn't. Factoring stopped after one or a few small factors and the rest of the tiny factors was found only at a rather ridiculous level of 80-81 bits. There is a huge amount of candidates that have unreported factors at the reported bit level. You can easily check this premise.

=> The statistics drawn from this set will be severely flawed unless a sophisticated model is built and fitted. I wholeheartedly recommend the home-grown statisticians (armed with Excel and four basic arithmetic operations) to stop plotting number towers and drawing barcharts and then kowtowing to them.

Notice that http://www.mersenne.ca/manyfactors.php 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.

It is clear that if we show the number of Mersenne numbers with only 1 known prime factor, that set would be overrepresented, because most factorizations stop when the first prime factor is known (other prime factors do not help GIMPS). But this is not the case.

[alpertron]

Originally Posted by R.D. Silverman

Indeed. Being stupidly argumentative (from ignorance) with someone who
knows a lot more than you is equally offensive and disrespectful.

Or maybe you argued with your teachers when you were younger?

His remarks were made in order to be provocative. That too is offensive.

I teach in the University (you can find that by searching on Internet if you want), and I know I'm not perfect. When one of my students finds that I made a mistake, I do not try to hide it saying that I'm the professor.

[xilman]

Originally Posted by R.D. Silverman

His remarks were made in order to be provocative. That too is offensive.

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