mersenneforum.org > Math 17-year-old proves new theorem related to Carmichael numbers
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 2022-10-14, 22:24 #1 joejoefla   May 2019 25 Posts The High Schooler Who Solved a Prime Number Theorem
 2022-10-14, 22:38 #2 Uncwilly 6809 > 6502     """"""""""""""""""" Aug 2003 101×103 Posts 101010100010002 Posts
2022-10-14, 23:17   #3
joejoefla

May 2019

25 Posts

Quote:
 Originally Posted by Uncwilly
Sorry!

 2022-10-14, 23:51 #4 ixfd64 Bemusing Prompter     "Danny" Dec 2002 California 46768 Posts 17-year-old proves new theorem related to Carmichael numbers
 2022-10-15, 03:51 #5 Uncwilly 6809 > 6502     """"""""""""""""""" Aug 2003 101×103 Posts 23×1,361 Posts
2022-10-15, 09:39   #6
sweety439

"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36

2×7×263 Posts

Quote:
 Originally Posted by ixfd64 https://quantamagazine.org/teenager-...likes-20221013
He proved that for every enough large number n, there is at least one Carmichael number between n and 2*n? (I think that n=3301 is enough large)

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 2022-10-15 at 09:39

2022-10-15, 16:38   #7
LaurV
Romulan Interpreter

"name field"
Jun 2011
Thailand

1027310 Posts

Quote:
 Originally Posted by sweety439 (I also have a conjecture: For every n>1, there is at least one twin prime pair between n and 3*n exclusive)
You have first to prove you have enough twin pairs. Maybe there is only a limited (i.e. finite) number of them?
(at least for Carmichael numbers, we knew there are enough of them...)

2022-10-15, 17:09   #8
R. Gerbicz

"Robert Gerbicz"
Oct 2005
Hungary

110010010112 Posts

Quote:
 Originally Posted by LaurV You have first to prove you have enough twin pairs. Maybe there is only a limited (i.e. finite) number of them?
False, but that is trivially true that if there is a twin prime in [n,2n] then there are infinitely many.
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.

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