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Old 2015-05-06, 16:03   #1
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Default Largest primes, location on critical line.

For the largest primes, is there a site that also lists their location on the critical line.
After a few quick internet searches I came up empty handed.

Does anyone know of such a site.
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Old 2015-05-06, 17:57   #2
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Quote:
Originally Posted by jwaltos View Post
For the largest primes, is there a site that also lists their location on the critical line.
After a few quick internet searches I came up empty handed.

Does anyone know of such a site.
Critical line?
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Old 2015-05-06, 18:11   #3
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Quote:
Originally Posted by xilman View Post
Critical line?


Critical Line

Quote:
The line R[s]=1/2 in the complex plane on which the Riemann hypothesis asserts that all nontrivial (complex) Riemann zeta function zeros lie.
edit2: at least that's what I found from quick google searching.

Last fiddled with by science_man_88 on 2015-05-06 at 18:12
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Old 2015-05-09, 11:51   #4
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There's no such thing as "primes on the critical line" (at least not the critical line that is generally known as "the critical line").

The nontrivial zeroes of the Riemann Zeta Function, with which the number of primes can be approximated, are conjectured to be on the critical line, but there's no direct mapping that links these zeroes to the primes themselves.
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Old 2015-05-10, 02:57   #5
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The association I intended was concerning the non-trivial zeros wrt to the Riemann zeta function.
When "critical line" and "prime numbers" were used in the same sentence I assumed this would reference the hypothesis adequately. Matt, you're correct in the literal sense that what I stated had no meaning; the function works in aggregate.
If the R.H. was proven as correct, all primes would be countable within any range and associated with non-trivial zeros on the critical line. I'm not trying to prove the hypothesis but rather trying to understand aspects of it. Non-primes are not countable within the zeta function (except by inference) meaning that the largest primes are denumerable. Is the density of the smaller primes and their contribution to the non-trivial zeros relative to the sparseness of the largest primes and their contribution separable and distinctive such that the largest primes "can almost be seen to map directly" to the critical line? For my purposes, I had developed a `cyclotomic-like` expression mapping several million sequential primes. The graph (using Curve Expert Pro) of these initial millions of points was smooth but not monotonic. I also examined sets of (much) larger sequential primes. Studying Chebotarev's results and complementary theoretical associations provided little additional insight. Since I was stuck, I thought I would ask a question.

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Old 2015-05-11, 04:02   #6
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Default A couple of dated files.

I hope these visuals assist my prior post which was far too simple to do justice to what is a very challenging topic.
Both graphs depict sequential primes of a specific form using a simple equation. The same parameters were used in both cases; as these are dated I have progressed a bit beyond what is shown. When the parameters are adjusted on sequential sections of primes, a graph similar to the first smooth progression will result.
Splicing these results and interpolating provides a simple functional description for large swaths of primes of all forms but the technical justification is lacking.
As an analogy, consider a head of hair where each strand represents a sequence of primes of a specific modulus. Combing the hair will create a nice smooth style but will do nothing to explain the raison d'etre of the hair.
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Old 2015-05-11, 13:35   #7
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Quote:
Originally Posted by jwaltos View Post
When "critical line" and "prime numbers" were used in the same sentence I assumed this would reference the hypothesis adequately. Matt, you're correct in the literal sense that what I stated had no meaning
You assumed incorrectly, for the reason Matt gave.
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Old 2015-05-11, 15:07   #8
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With all due respect, yes.
As a working professional in this field (as opposed to those who do not earn their livelihood in this field), when you discuss a topic with a peer or collegue there is a level of understanding that is assumed, otherwise, you are providing a lesson or a lesson is being provided to you. A specific jargon (not a bad thing) referencing appropriate technical mathematical terms relating applicable theorems and lemmas must be within the toolkit of the conversing particants, otherwise, the `information transfer` is degraded. Visual or symbolic (topologist or algebraist), general member or specialized professional [of this forum], we may think about the same things but we will express them differently according to our lexicon. (aside: Dyson should have received a Nobel for his work. I was assuming something here which I will make explicit, he demonstrated the equivalence of two different formulations of QED but did not share in the Nobel. (I'm not a physicist.)). If you know of the Sapir-Whorf hypothesis, then you will understand my point (I'm not a linguist.). I prefer not to make mistakes, but when pointed out, I will correct them.
Let me ask you this, if you knew that I had a Ph.D in algebraic topology (I don't.), would you have responded as you had? Matt corrected me directly. You did something else.

Last fiddled with by jwaltos on 2015-05-11 at 15:59 Reason: correction
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Old 2015-05-11, 18:30   #9
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Quote:
Originally Posted by jwaltos View Post
Let me ask you this, if you knew that I had a Ph.D in algebraic topology (I don't.), would you have responded as you had?
I believe I would. I neither assumed that you had such a degree nor assumed that you did not. I did assume that you knew what you were talking about.

If I knew that you had that degree I would have assumed that you were discussing some other critical line about which I knew nothing and would have asked for clarification as to which line, which is exactly what I did. I accept that my question was rather terse.
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Old 2015-05-11, 21:40   #10
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Completely fair.
I presumed a slight where none existed. If I had an advanced degree and had written the original post I probably would not have been as generous in my assessment. Thanks for the quick reply.
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