August 18th, 2017, 10:12 AM  #41 
Senior Member Joined: Sep 2015 From: USA Posts: 1,790 Thanks: 923 
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 10:14 AM. 
August 18th, 2017, 10:17 AM  #42 
Senior Member Joined: Aug 2012 Posts: 1,780 Thanks: 482  The $n1$ consecutive positive integers from $n! + 2$ to $n! + n$ contain no primes. In other words there are arbitrarily large prime gaps.
Last edited by Maschke; August 18th, 2017 at 10:34 AM. 
August 18th, 2017, 11:32 AM  #43  
Math Team Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,372 Thanks: 233  Quote:
Chebyshev said it, but I'll say it again; There's always a prime between n and 2n. Then there was Paul ErdÃ¶s ... https://en.m.wikipedia.org/wiki/Paul_Erd%C5%91s Last edited by agentredlum; August 18th, 2017 at 11:40 AM.  
August 20th, 2017, 09:30 PM  #44 
Banned Camp Joined: Dec 2012 Posts: 1,028 Thanks: 24  Are numbers I invented as a Bijection with all $P\in \mathbb{N^+}$. Are made as a pure power, I call Integer nth 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 $M_n=(x^n(x1)^n)$ 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 . 2x1 = 1 . 51 = 4 2 . 2x1 = 3 . 43 = 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 . 2x1 = 5 . 15 = 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 07:36 PM. 
August 21st, 2017, 02:13 AM  #45 
Banned Camp Joined: Dec 2012 Posts: 1,028 Thanks: 24 
Here an example of how my Complicate Numbers can be shown on a TwoHandClock: 
August 21st, 2017, 10:31 AM  #46  
Senior Member Joined: Sep 2015 From: USA Posts: 1,790 Thanks: 923  Quote:
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.  
August 21st, 2017, 11:23 AM  #47 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,767 Thanks: 1017 Math Focus: Elementary mathematics and beyond  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 
August 21st, 2017, 06:07 PM  #48 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,767 Thanks: 1017 Math Focus: Elementary mathematics and beyond 
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. 
August 21st, 2017, 08:53 PM  #49 
Banned Camp Joined: Dec 2012 Posts: 1,028 Thanks: 24 
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. Thanks ciao Stefano 
August 21st, 2017, 09:11 PM  #50  
Math Team Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,372 Thanks: 233  Quote:
Perhaps we should refrain from making all encompassing derogatory statements against the OP?  

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