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 2015-09-08, 17:48 #1 wildrabbitt   Jul 2014 1BF16 Posts probabilistic number theory Hi, I totally stuck as to how this conclusion was reached and would be forever grateful if someone can explain the reasoning. The problem concerns this page : http://www.mersenneforum.org/attachm...1&d=1441734205 The step I do not understand is this bit : http://www.mersenneforum.org/attachm...1&d=1441734205 My understanding is that P({m}) is the probability that a positive integer is divisible by m and this is less than the probability that a number is not divisible by any of the primes for which m < p <= n. That's the bit I don't understand : why is this statement true? Attached Thumbnails
2015-09-08, 18:53   #2
R. Gerbicz

"Robert Gerbicz"
Oct 2005
Hungary

1,531 Posts

Quote:
 Originally Posted by wildrabbitt The step I do not understand is this bit : http://www.mersenneforum.org/attachm...1&d=1441734205 My understanding is that P({m}) is the probability that a positive integer is divisible by m and this is less than the probability that a number is not divisible by any of the primes for which m < p <= n. That's the bit I don't understand : why is this statement true?
No. P({m}) is the measure (probability) of one single integer=m.
Hence the inequality is a triviality as m has no prime divisor greater than m.

 2015-09-08, 20:08 #3 wildrabbitt   Jul 2014 1BF16 Posts Thanks very much.
 2015-09-12, 09:03 #4 wildrabbitt   Jul 2014 3×149 Posts clarification So P({m}) is the probability that a positive integer randomly chosen from the infinitude of postive integers is m?
2015-09-15, 13:17   #5
R.D. Silverman

Nov 2003

22×5×373 Posts

Quote:
 Originally Posted by wildrabbitt So P({m}) is the probability that a positive integer randomly chosen from the infinitude of postive integers is m?
And you think that you can prove Erdos-Turan????

You need to take a basic course in probability and statistics. You might then realize

 2015-09-15, 13:31 #6 wildrabbitt   Jul 2014 3×149 Posts I've got an A at A-level Mathematics - Pure and Statistics. I've been studying mathematics for 4 years as a part time student with the Open University where we study in isolation seeing tutors maybe 3 times in the duration of a 7 months module unlike the priveledged place university students. I got 78% on the first semester exam at the University of East Anglia where I was studying for 6 months but left for health reasons hence why I'm now studying with the Open University. I've got 6000+ GHz days of LL test time on the GIMPS. Why would you rather patronise me than answer a question I have about proababilistic number theory to do with something I read in a post-graduate advanced mathematics book when I don't yet have a degree ? What has proabailisitic number theory got to do with the Erdos-Turan conjecture? Last fiddled with by wildrabbitt on 2015-09-15 at 13:31
 2015-09-15, 14:01 #7 wildrabbitt   Jul 2014 3×149 Posts I think the answer to my first question is that you can't imagine yourself ever solving anything unsolved so presume that an enquirer like me couldn't possibly either. Last fiddled with by wildrabbitt on 2015-09-15 at 14:01
2015-09-15, 14:21   #8
R.D. Silverman

Nov 2003

22×5×373 Posts

Quote:
 Originally Posted by wildrabbitt I've got an A at A-level Mathematics - Pure and Statistics. I've been studying mathematics for 4 years as a part time student with the Open University where we study in isolation seeing tutors maybe 3 times in the duration of a 7 months module unlike the priveledged place university students.
And then you ask questions about a random sampling from all of Z+??????
You clearly did not learn the subject.

It is trivially impossible to select an integer uniformly at random from Z+!!!!!! The density function
does not exist!

BTW the John Baez crankometer gives a lot of points for claiming that one attended school as if
this claim were evidence of sanity......

Quote:
 What has proabailisitic number theory got to do with the Erdos-Turan conjecture?
Hint: Ergodic theory. Tauberien theory.

Furthermore your nonsensical question shows that your understanding of basics is weak.
Yet you presume to try to prove something that Erdos and Turan could not??

Before one tries to prove an outstanding problem whose solution has evaded the best mathematicians
so far one should at least do a fair bit of reading about what is currently known and what techniques
have already been tried. Your query about the problem makes it clear that you failed due diligence

Arrogance and ignorance are a bad combination.

Last fiddled with by R.D. Silverman on 2015-09-15 at 14:35

2015-09-15, 14:27   #9
R.D. Silverman

Nov 2003

11101001001002 Posts

Quote:
 Originally Posted by R.D. Silverman And then you ask questions about a random sampling from all of Z+?????? You clearly did not learn the subject. It is trivially impossible to select an integer uniformly at random from Z+!!!!!! The density function does not exist! BTW the John Baez crankometer gives a lot of points for claiming that one attended school as if this claim were evidence of sanity...... Hint: Ergodic theory. Tauberien theory. Furthermore your nonsensical question shows that your understanding of basics is weak. Yet you presume to try to prove something that Erdos and Turan could not?? Arrogance and ignorance are a bad combination.
The techniques of Green-Tao may be a starting point for proving the full Erdos-Turan problem.

Last fiddled with by R.D. Silverman on 2015-09-15 at 14:28

2015-09-15, 15:19   #10
R.D. Silverman

Nov 2003

22×5×373 Posts

Quote:
 Originally Posted by wildrabbitt I think the answer to my first question is that you can't imagine yourself ever solving anything unsolved so presume that an enquirer like me couldn't possibly either.
Classic Dunning & Kruger.

Before I try to solve an unsolved problem that has eluded others I make it a point
to STUDY THE PROBLEM.

Your query made it clear that you know so little about the problem that any claim you make
that you attempted a proof is sheer arrogance.

 2015-09-15, 15:57 #11 wildrabbitt   Jul 2014 3·149 Posts Discoveries aren't made by humble people. - according to "Hardy" I claim to have tried to answer the Erdos-Turan conjecture because I have tried to. You can call it arrogance. I've never read anything humble written by you here. I guess having being diagnosed mentally ill I'm susceptable to delusions of grandeur but when I get bored of solving trivial maths problems I need something more exciting and I think of the likes of Cantor, Godel and John Nash so I can put up with the delusions. I've been to Cambridge and bought a book on Probabilistic Number Theory. I've bought a book by Erdos to study so I can find out more about the problem. I'm enquiring here on mersenne.org about the problem so that can clear things up for myself. I'm studying the problem according to me. You use the words "I make a point to STUDY THE PROBLEM". I use the phrase "I make a point" to show that I respect something. e.g I make a point to be polite to my tutors when I email them. Why do you make a point?

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