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Old 2022-10-14, 22:24   #1
joejoefla
 
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Default The High Schooler Who Solved a Prime Number Theorem

https://www.youtube.com/watch?v=Kqi_6v2RGB0
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Old 2022-10-14, 22:38   #2
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Old 2022-10-14, 23:17   #3
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Sorry!
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Old 2022-10-14, 23:51   #4
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Default 17-year-old proves new theorem related to Carmichael numbers

https://quantamagazine.org/teenager-...likes-20221013
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Old 2022-10-15, 03:51   #5
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Old 2022-10-15, 09:39   #6
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Originally Posted by ixfd64 View Post
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
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Old 2022-10-15, 16:38   #7
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(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...)
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Old 2022-10-15, 17:09   #8
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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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