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August 18th, 2017, 11:12 AM   #41
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Now that I think about, and given my ignorance of the deep properties of the prime numbers, I'm not certain that the spacing of adjacent primes is in fact bounded.

Perhaps some of you deep number theory thinkers can comment.

Incidentally this concept is apparently given the name "Prime Gap" and has been extensively studied.

Last edited by romsek; August 18th, 2017 at 11:14 AM.
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August 18th, 2017, 11:17 AM   #42
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Originally Posted by romsek View Post
Now that I think about, and given my ignorance of the deep properties of the prime numbers, I'm not certain that the spacing of adjacent primes is in fact bounded.
The $n-1$ consecutive positive integers from $n! + 2$ to $n! + n$ contain no primes. In other words there are arbitrarily large prime gaps.
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Last edited by Maschke; August 18th, 2017 at 11:34 AM.
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August 18th, 2017, 12:32 PM   #43
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Originally Posted by Maschke View Post
The $n-1$ consecutive positive integers from $n! + 2$ to $n! + n$ contain no primes. In other words there are arbitrarily large prime gaps.
To me this has always been fascinating because the number of primes is infinite ... infinities swallowed up by other infinities <--- my humble opinion


Chebyshev said it, but I'll say it again; There's always a prime between n and 2n.

Then there was Paul Erdös ...

https://en.m.wikipedia.org/wiki/Paul_Erd%C5%91s

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Last edited by agentredlum; August 18th, 2017 at 12:40 PM.
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August 20th, 2017, 10:30 PM   #44
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Originally Posted by cjem View Post
What do you mean by "complicate numbers"?
Are numbers I invented as a Bijection with all $P\in \mathbb{N^+}$.

Are made as a pure power, I call Integer n-th Root of $P$, plus a $Rest$:

For example taking $n=2$:

$1 = 1^2+0 = 1M_2+0 $
$2= 1^2+1 = 1M_2+1 $
$3= 1^2+2 = 1M_2+2 $
$4= 2^2+0 = 2M_2+0 $
$5= 2^2+0 = 2M_2+1 $

Where $M_n=(x^n-(x-1)^n)$ since you can find the Integer Root as a recoursive difference using this function as Modulo:

For example Square root of 5 is equal to make it modulo $M_2$:

1 . 2x-1 = 1 . 5-1 = 4
2 . 2x-1 = 3 . 4-3 = 1 so 2 is the Integer Square Root of 5, so 5= 2^2+1

in fact if you can't go over because:

3 . 2x-1 = 5 . 1-5 = -4

And the same using a special trick to go in $Q$

etc...

I'm writing a book on, but you find that in several of my post here.


And lot must be written on

Last edited by skipjack; August 21st, 2017 at 08:36 PM.
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August 21st, 2017, 03:13 AM   #45
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Here an example of how my Complicate Numbers can be shown on a Two-Hand-Clock:


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August 21st, 2017, 11:31 AM   #46
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Here an example of how my Complicate Numbers can be shown on a Two-Hand-Clock:
No one cared when you posted this last time and no one cares now.

Why don't you start you own forum where you can post all your ideas and then you can post comments about how how incredible they are and how the author must be a super genius.
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August 21st, 2017, 12:23 PM   #47
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complicatemodulus,

I've been trying to make a shred of sense out of all of this but I fail to see what relevance it has. You've repeatedly given vague (if any) explanations of your ideas and usually include some other terminology that you've made up - undefined - in your explanation. I'm closing this thread and I will delete any further comments you make in other threads until this issue is addressed to the satisfaction of most of us. If you cannot do this - don't post.

Thank you,

greg1313
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August 21st, 2017, 07:07 PM   #48
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I've decided to reopen the thread to allow discussion of the OP by all concerned members. Aside from this, what I posted above still stands.

Thank you for your patience and good evening.
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August 21st, 2017, 09:53 PM   #49
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I think we all agree on the point:

talking of primes, the use of the word "random" is ambiguos, than is better to avoid it.

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Stefano
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August 21st, 2017, 10:11 PM   #50
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Originally Posted by greg1313 View Post
I've decided to reopen the thread to allow discussion of the OP by all concerned members. Aside from this, what I posted above still stands.

Thank you for your patience and good evening.
I'm glad you reopened the thread because I find his postings interesting from a Number Theoretic point of view. It is true in my opinion that there is a language barrier.

Perhaps we should refrain from making all encompassing derogatory statements against the OP?

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