20150908, 17:48  #1 
Jul 2014
450_{10} 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? 
20150908, 18:53  #2  
"Robert Gerbicz"
Oct 2005
Hungary
3113_{8} Posts 
Quote:
Hence the inequality is a triviality as m has no prime divisor greater than m. 

20150908, 20:08  #3 
Jul 2014
2×3^{2}×5^{2} Posts 
Thanks very much.

20150912, 09:03  #4 
Jul 2014
2×3^{2}×5^{2} Posts 
clarification
So
P({m}) is the probability that a positive integer randomly chosen from the infinitude of postive integers is m? 
20150915, 13:17  #5  
"Bob Silverman"
Nov 2003
North of Boston
7508_{10} Posts 
Quote:
You need to take a basic course in probability and statistics. You might then realize that your question is nonsense. 

20150915, 13:31  #6 
Jul 2014
450_{10} Posts 
I've got an A at Alevel 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 postgraduate advanced mathematics book when I don't yet have a degree ? What has proabailisitic number theory got to do with the ErdosTuran conjecture? Last fiddled with by wildrabbitt on 20150915 at 13:31 
20150915, 14:01  #7 
Jul 2014
2·3^{2}·5^{2} 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 20150915 at 14:01 
20150915, 14:21  #8  
"Bob Silverman"
Nov 2003
North of Boston
1110101010100_{2} Posts 
Quote:
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:
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 before attempting your "proof" Arrogance and ignorance are a bad combination. Last fiddled with by R.D. Silverman on 20150915 at 14:35 

20150915, 14:27  #9  
"Bob Silverman"
Nov 2003
North of Boston
1110101010100_{2} Posts 
Quote:
Last fiddled with by R.D. Silverman on 20150915 at 14:28 

20150915, 15:19  #10  
"Bob Silverman"
Nov 2003
North of Boston
2^{2}×1,877 Posts 
Quote:
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. 

20150915, 15:57  #11 
Jul 2014
2·3^{2}·5^{2} Posts 
Discoveries aren't made by humble people.  according to "Hardy"
I claim to have tried to answer the ErdosTuran 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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