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June 16th, 2013, 11:19 PM   #1
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True or not

Hello!
If where are two prime numbers consecutive then there is the inequality .
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June 17th, 2013, 10:34 PM   #2
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Re: True or not

Hello!
If the inequality is true then the inequality of problem is true.
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June 18th, 2013, 05:49 AM   #3
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Re: True or not

Quote:
Originally Posted by Dacu
If the inequality is true then the inequality of problem is true.
I haven't checked this reduction but I believe it to be true using a conditional bound which can be shown to be smaller than 2 initially with any small value and then using the fact that it is decreasing.
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June 18th, 2013, 06:10 AM   #4
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Re: True or not

Quote:
Originally Posted by mathbalarka
Quote:
Originally Posted by Dacu
If the inequality is true then the inequality of problem is true.
I haven't checked this reduction but I believe it to be true using a conditional bound which can be shown to be smaller than 2 initially with any small value and then using the fact that it is decreasing.
Hello!
I don't understand the idea.Please give details.
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June 18th, 2013, 06:13 AM   #5
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Re: True or not

Quote:
Originally Posted by Dacu
I don't understand the idea.
What's not to understand? I have shown that this inequality is conditionally true assuming Andrica's conjecture.
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June 18th, 2013, 06:17 AM   #6
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Re: True or not

It can be proven with the famous theorem of Hoheisel that there are only finitely many counterexamples.
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June 18th, 2013, 06:18 AM   #7
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Re: True or not

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Originally Posted by mathbalarka
What's not to understand? I have shown that this inequality is conditionally true assuming Andrica's conjecture.
You should definitely state that you're using something like Andrica! That's far beyond our ability to prove at the moment and doesn't even follow from RH.
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June 18th, 2013, 06:25 AM   #8
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Re: True or not

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That's far beyond our ability to prove at the moment and doesn't even follow from RH.
Yes, but I never claimed I had a proof, did I? I showed how this inequality almost surely holds.

Quote:
Originally Posted by CRGreathouse
It can be proven with the famous theorem of Hoheisel that there are only finitely many counterexamples.
Hmm, it never occurred to me. Oh well!
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June 18th, 2013, 07:16 AM   #9
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Re: True or not

I do not understand!From I do not see how it would result .
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June 18th, 2013, 07:20 AM   #10
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Re: True or not

Quote:
Originally Posted by Dacu
From . . .
This is not Hoheisel's result.
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