20140316, 13:20  #1 
Jun 2005
373 Posts 
Elementary Literature on probabilistic aspects of prime searching
Hello folks,
I fire up my account after a long time. Next semester, I am going to teach a seminar on probability for future teachers for primary schools and schools which go until 10th grade (Haupt und Realschule in Germany). These future teachers know less about mathematics than one would hope, but they are motivated, and I would like to teach something that they might be able to use later, and that still has some mathematical background. I am a probabilist, and know virtually nothing about number theory. But this not going to stop me. A few ideas I had were
The literature should be readable with very basic undergraduate level understanding of mathematics. If in german, that would help some of them. I would rather have them do something below their potential than giving them something they cannot chew. Any hints and comments are very much appreciated, also on different probabilistic topics. Cheers, H. 
20140316, 15:23  #2  
Bamboozled!
"πΊππ·π·π"
May 2003
Down not across
3^{3}×389 Posts 
Quote:
Nice intro at https://de.wikipedia.org/wiki/Satz_von_Bayes Last fiddled with by xilman on 20140316 at 15:25 Reason: Add url 

20140316, 17:17  #3  
Jun 2005
373 Posts 
Quote:
Quote:


20140316, 17:39  #4  
Bamboozled!
"πΊππ·π·π"
May 2003
Down not across
3^{3}·389 Posts 
Quote:
If you're doing P1 and ECM, you should also do P+1. The likelihood of needing n dependencies from the linear algebra in NFS, QS, etc, to find the prime factors of N. This is trickier than it sounds. I'll explain why if it's not obvious to you. Probability of N being psmooth  related to ECM as you already note, but also to sieving algorithms. Extend to case where N/P (where P is psmooth) has a small number of factors all of which are less than q (the socalled large prime). 

20140316, 20:12  #5  
Account Deleted
"Tim Sorbera"
Aug 2006
San Antonio, TX USA
17·251 Posts 
Quote:
Also of note in this area: https://en.wikipedia.org/wiki/Poisson_distribution As one who learned much about probability through my prime searches, I can say that understanding Poisson probabilities is a major part of it: it helps make sense of the random event of finding a prime. Sorry I can't recommend specific literature for the class, I learned through online resources. Last fiddled with by MiniGeek on 20140316 at 20:13 

20140317, 17:34  #6  
Nov 2003
2^{2}·5·373 Posts 
Quote:
may be of help. Elliott's book may help as well. 

20140317, 18:19  #7 
Aug 2006
3·1,987 Posts 

20140318, 14:37  #8  
Jan 2014
38_{10} Posts 
Quote:
(If anyone wants it, you can send me a private message.) 

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