My Math Forum Proof Primes are not "random"

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August 17th, 2017, 09:11 AM   #31
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Quote:
 Originally Posted by complicatemodulus The worrd "random" was used several time in Sautoy books.
What is the definition in those books? I haven't read them.

Random could mean:

* Non-deterministic. Not the output of any Turing machine. Or

* Statistically random. Satisfies some particular technical definition of randomness, regardless of whether the sequence is deterministic or not. Or

* Computationally inefficient. I've never heard "random" used that way but a couple of posters in this thread seem to be using it like that.

What do YOU mean by random? Please be specific.

 August 17th, 2017, 09:34 AM #32 Banned Camp   Joined: Dec 2012 Posts: 1,028 Thanks: 24 Sorry, I hope it was clear: The word "random" was wrongly used by Sautoy as "unpredictable" since he is just trying to phishing fish... This is the point I would like to underline with my concerning... The "book" is: "primes enigma" I don't know if there is an english version.
 August 17th, 2017, 09:40 AM #33 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,958 Thanks: 1146 Math Focus: Elementary mathematics and beyond With a good look I would think the primes are statistically random. You may be able to determine the "next prime" deterministically but it can't be inferred from the distribution of the previous primes, can it?
August 17th, 2017, 09:46 AM   #34
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Quote:
 Originally Posted by complicatemodulus Sorry, I hope it was clear: The word "random" was wrongly used by Sautoy as "unpredictable" since he is just trying to phishing fish... This is the point I would like to underline with my concerning...
That's not answering the question. You were asked what you mean by "random" in the OP.

August 17th, 2017, 12:35 PM   #35
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Quote:
 Originally Posted by greg1313 With a good look I would think the primes are statistically random. You may be able to determine the "next prime" deterministically but it can't be inferred from the distribution of the previous primes, can it?
However, given a range of consecutive numbers, I can give a close approximation to how many primes there are!

August 17th, 2017, 07:51 PM   #36
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Quote:
 Originally Posted by complicatemodulus The word "random" was wrongly used by Sautoy as "unpredictable" since he is just trying to phishing fish...
Marcus du Sautoy, being a highly eminent professor of mathematics and native English speaker, is unlikely to have used the word "random" wrongly. I'll trust his word over that of anybody on this forum. But he might not have been using it in a strictly technical sense if the book is aimed at a more popular audience than purely mathematicians.

Last edited by v8archie; August 17th, 2017 at 08:40 PM.

 August 17th, 2017, 08:10 PM #37 Senior Member   Joined: Aug 2012 Posts: 2,354 Thanks: 735 Oh he's a contemporary mathematician. Hadn't heard of him. Thanks all for the reference. https://en.wikipedia.org/wiki/Marcus_du_Sautoy So OP, what specific book and what specific page on that book contains the word random; and are there any definitions of what random means in a few of the preceding pages? Also note that his Wiki page says he's involved in popularization of math; so as someone noted, he might be waving his hands a little for a nontechnical audience. We do need to know the context of the quote. Last edited by Maschke; August 17th, 2017 at 08:12 PM.
August 17th, 2017, 09:34 PM   #38
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Quote:
 Originally Posted by Maschke Oh he's a contemporary mathematician. Hadn't heard of him. Thanks all for the reference. https://en.wikipedia.org/wiki/Marcus_du_Sautoy So OP, what specific book and what specific page on that book contains the word random; and are there any definitions of what random means in a few of the preceding pages? Also note that his Wiki page says he's involved in popularization of math; so as someone noted, he might be waving his hands a little for a nontechnical audience. We do need to know the context of the quote.
He is playing with non math readers leaving an halo of mistery about primes.

Once again: I'm playing with "random" word too, since is clear that they are well fixed and sorted, but we can lay the trick, for example asking if the next prime will be right or left respect the previous medium behavior, and the collection of a large number of primes will said us it is close to fifty-fifty.... etc...

But I hope the focus will be on the other result using complicate numbers on what nobody say a word...

August 18th, 2017, 08:10 AM   #39
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Quote:
 Originally Posted by complicatemodulus But I hope the focus will be on the other result using complicate numbers on what nobody say a word...
What do you mean by "complicate numbers"?

 August 18th, 2017, 09:53 AM #40 Senior Member     Joined: Sep 2015 From: USA Posts: 2,529 Thanks: 1389 A much better, imo, way to phrase the problem is "Is the spacing of adjacent primes a random variable?" As someone earlier in the thread noted once you satisfy the axioms of the natural numbers the primes and their separation are fixed. They aren't random. Given that one can ask. "Does the spacing of adjacent primes satisfy the properties of pseudo-random numbers?" The properties are pseudo-random numbers are well known. Another important question is "Is the implied distribution of the spacing of adjacent primes within a bounded subset of them independent of the location of the subset?" This is the equivalent to the ergodicity of a time series. Finally an important question is "Does the implied distribution of the spacing of adjacent primes within a subset of all primes converge as we let the subset grow to include all primes. Knowing the properties of the primes we know that the spacing of adjancent primes is bounded. (I think) Thus we have a finite series of values that we can trivially assign probabilities to to achieve a distribution. The other questions are less trivial.

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