20221014, 22:24  #1 
May 2019
2^{5} Posts 
The High Schooler Who Solved a Prime Number Theorem

20221014, 22:38  #2 
6809 > 6502
"""""""""""""""""""
Aug 2003
101×103 Posts
10101010001000_{2} Posts 

20221014, 23:17  #3  
May 2019
2^{5} Posts 
Quote:


20221014, 23:51  #4 
Bemusing Prompter
"Danny"
Dec 2002
California
4676_{8} Posts 
17yearold proves new theorem related to Carmichael numbers

20221015, 03:51  #5 
6809 > 6502
"""""""""""""""""""
Aug 2003
101×103 Posts
2^{3}×1,361 Posts 

20221015, 09:39  #6  
"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36
2×7×263 Posts 
Quote:
Like Chebyshev's theorem: For every n>1, there is at least one prime between n and 2*n exclusive (I also have a conjecture: For every n>1, there is at least one twin prime pair between n and 3*n exclusive) Last fiddled with by sweety439 on 20221015 at 09:39 

20221015, 16:38  #7  
Romulan Interpreter
"name field"
Jun 2011
Thailand
10273_{10} Posts 
Quote:
(at least for Carmichael numbers, we knew there are enough of them...) 

20221015, 17:09  #8  
"Robert Gerbicz"
Oct 2005
Hungary
11001001011_{2} Posts 
Quote:
And notice that it is even the case for the proof of Chebyshev theorem from Paul Erdos. To give a much weaker theorem: there is a prime between m and 2^m, for this use the Fermat number F(n)=2^(2^n)+1 for n=ceil(log2(m))2. (the rest is homework). And for this we are not using that there are infinitely many primes, but reaching a "Chebyshev type" result, and from that follows that there are infinitely many primes. 

Thread Tools  
Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Carmichael numbers  devarajkandadai  Number Theory Discussion Group  14  20171115 15:00 
Carmichael Numbers  Stan  Miscellaneous Math  19  20140102 21:43 
Carmichael numbers (M) something  devarajkandadai  Miscellaneous Math  2  20130908 16:54 
Carmichael Numbers  devarajkandadai  Miscellaneous Math  0  20060804 03:06 
Carmichael Numbers II  devarajkandadai  Math  1  20040916 06:06 