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Mathematician pair find prime numbers aren't as random as thought

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  Mathematician pair find prime numbers aren't as random as thought Sam Wormley <swormley1@gmail.com> - 2016-03-15 20:16 -0500
    Re: Mathematician pair find prime numbers aren't as random as thought "hanson" <hanson@quick.net> - 2016-03-15 18:46 -0700
      Re: Mathematician pair find prime numbers aren't as random as thought Fabian Russell <fb@zen.info> - 2016-03-16 10:02 +0000
        Re: Mathematician pair find prime numbers aren't as random as thought "hanson" <hanson@quick.net> - 2016-03-16 10:24 -0700
    Re: Mathematician pair find prime numbers aren't as random as thought Jamie M <jmorken@shaw.ca> - 2016-03-15 19:50 -0700
      Re: Mathematician pair find prime numbers aren't as random as thought noTthaTguY <abu.kuanysh05@gmail.com> - 2016-03-16 14:11 -0700
    Re: Mathematician pair find prime numbers aren't as random as thought David Bernier <david250@videotron.ca> - 2016-03-16 19:02 -0400
      Re: Mathematician pair find prime numbers aren't as random as thought The Starmaker <starmaker@ix.netcom.com> - 2016-03-16 23:38 -0800

#562739 — Mathematician pair find prime numbers aren't as random as thought

Mathematician pair find prime numbers aren't as random as thought
> http://phys.org/news/2016-03-mathematician-pair-prime-random-thought.html

> (Phys.org)—A pair of mathematicians with Stanford University has
> found that the distribution of the last digit of prime numbers are
> not as random as has been thought, which suggests prime's themselves
> are not. In their paper uploaded to the preprint server arXiv, Robert
> Lemke Oliver and Kannan Soundararajan describe their study of the
> last digit in prime numbers, how they found it to be less than
> random, and what they believe is a possible explanation for their
> findings.
>


Unexpected biases in the distribution of consecutive primes
> http://arxiv.org/abs/1603.03720

> While the sequence of primes is very well distributed in the reduced
> residue classes (mod q), the distribution of pairs of consecutive
> primes among the permissible ϕ(q)2 pairs of reduced residue classes
> (mod q) is surprisingly erratic. This paper proposes a conjectural
> explanation for this phenomenon, based on the Hardy-Littlewood
> conjectures. The conjectures are then compared to numerical data, and
> the observed fit is very good.

-- 

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#562742

"Sam Wormley" <swormley1@gmail.com> wrote:
> Mathematician pair find prime numbers aren't as random as thought
>> http://phys.org/news/2016-03-mathematician-pair-prime-random-thought.html
wherein the salient and operative lines are:
<edited for brevity and clarity>
>
"Just as Einstein's theory of relativity is a ***more complicated
version** of Newton's theory of gravity, the Hardy-Littlewood's
k-tuple conjecture is essentially the assumption that primes
are random which holds for  99% of the time but you need
that last 1% to make it valid, which is seen by this last-digit
k-tuple pattern, that place restrictions on to where the last
digit of each prime can fall.
>
What's more, as the primes stretch to infinity, they do eventually
shake off the pattern & give the random distribution as expected"
...  just like in Einstein' theory which is expected to hold at
very large values where dilations and contraction go towards
infinity, but where restriction come into place for where the results
may fall.
>
This then makes Einstein Relativity conjectures to be just like this
k-tuple, which IOW makes Einstein;'s Relativity out to be totally
USELESS for any practical purpose in the real world and it
descends into the  reams of philosophy where religious undertones
arise that manifest themselves by Einstein Dingleberries
who worship  Albert's Sphincter... Pity, but ....    ROTFLMAO

> 

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#562794

On Tue, 15 Mar 2016 18:46:55 -0700, hanson wrote:

>
>  which IOW makes Einstein;'s Relativity out to be totally
> USELESS for any practical purpose in the real world
>

Radar guns -- relativistic doppler effect

cathode ray tubes -- relativistic electron velocity

Global positioning -- both SR and GR *must* be a foundation to
the technology

General magnetism -- relativity in the flesh

mass-energy equivalence (E=mc^2) -- nuclear energy power plants

These common, everyday applications of relativity completely
overturn your outlandish assertion.

>
> and it
> descends into the  reams of philosophy where religious undertones
> arise
>

Where the fuck does this gibberish arise?

Your entire post, in spite of its colloquial tone, is entirely
philosophical in nature.  For those without a leg to stand on,
philosophy is the only crutch.

Incidentally, the correct term is "realm" and not "ream."

The word "ream" refers to the act of inserting objects into
the ass.  I suppose the unconscious typo reveals your true
orientation.

LOL!  What a faggot loser!

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#562866

"Fabian Russell" <root@localhost.localdomain> aka
"Fagie Bodaisky", is a NY kike, who lives off the
tips he gets from being a rest-room attendant in a
NY Bath house for gay Jews.
>
Then Fagie bragged to augment his meager income 
by Fagie being a "photographer" who conducted 
nefarious acts against the US Infrastructure that
landed Fagie Bodaisky on a FBI watch list.
>
Fagie Bodaisky is also one of those many Einstein 
Dingleberries who read  Sci.Am. and then parrot buzz 
words about which Fagie knows less then a dog that
barks into the night at a distant noise he knows 
nothing about,  as can be seen when...
>
hanson wrote:
>> This k-tuple math conjectures then makes Einstein 
>> Relativity out to be totally USELESS for any practical 
>> purpose in the real world and it descends into the  
>> reams of philosophy where religious undertones
>> arise that manifest themselves by Einstein Dingleberries
>> who worship  Albert's Sphincter... 
> 
Fagie wrote:
> Radar guns -- relativistic doppler effect
> cathode ray tubes -- relativistic electron velocity
> General magnetism -- relativity in the flesh
> mass-energy equivalence (E=mc^2) -- nuclear energy power plants
> These common, everyday applications of relativity completely
> overturn your outlandish assertion.
>
hanson wrote:
That then is Fagie's delusional world of religiously
worshipping Einstein's Sphincter, wherewith a math 
description miraculously produces the above gizmos.
>
Every normal kid though knows that NONE of Fagie's
mentioned items require any SR/GR, not for their 
conception, nor their production, nor their manufacturing
nor their operation/s, nor their testing. Fagie has no
idea how R&D or Mfgr. works.... ahahahahaha...
>
Fagie mindlessly parroted on & wrote:
> Global positioning -- both SR and GR *must* be a 
> foundation to the technology
>
hanson wrote:
Fagie seeks refuge by referring to Ashby's tripe of "Relativity 
in the Global Positioning Systemin which it took Kike Ashby 
39 questionable & tortured steps to get to the 38 usec delay, 
when & while any high school student or engineer, can glean,
 for this particular situation, in 1 fell swoop, in ONE SINGLE 
STEP, in good, old Newtonian ways, and show that
>
|||||  ----  m_e/h * 2G/c^2 *86400  =  38...  microsec/day  ---- 
|||||  ---     m_e/h * 2G/c *86400  =  11.2... km drift/day   ---- 

where m_e = mass of earth and h = the satellite's height
above the earth surface. Correction are done by standard
industrial ways by classical methods devoid of any SR/GR.
< http://tinyurl.com/622an2>   or < http://tinyurl.com/57asbg>
>>
>>
||||| ---- GPS NEVER NEEDED neither SR nor GR ---- 
||||| not for its design, manufacturing, testing nor operations.
||||| ----------GPS was in operation  LONG before -------- 
|||||   Einstein Dingleberries came along to nuzzle into the
|||||   show, hoping to get some credit away from Newton.
>
But Fagie, the gay Einstein Dingleberry is too fanatical
in his worship of Einstein's sphincter, to see that he is
upfront & center, spreading his & hysteria with his
own and loud <http://tinyurl.com/Proof-of-Relativity
 
hanson wrote:
>> and Einstein's crap descends into the  reams of 
>> philosophy where religious undertones arise
>>
Fagie got irate and wondered:
> Where the fuck does this gibberish arise?
> Your entire post, in spite of its colloquial tone, is entirely
> philosophical in nature.  For those without a leg to stand on,
> philosophy is the only crutch.
>
hanson wrote:
Fagie, you are projection again. What you just said is 
exactly what you always do,since it is compulsively forced 
upon and out of you due to your obsession of religiously 
worshipping Albert's sphincter.., which is so fanatical that...
> 
Fagie made a Freudian slip & wrote:
> Incidentally, the correct term is "realm" and not "ream."
> The word "ream" refers to the act of inserting objects into
> the ass.  I suppose the unconscious typo reveals Fagie's
> true orientation . LOL!  What a faggot loser that Fagie is!
>
hanson wrote:
Fagie, thanks for he laughs though ... ahahahahahahnson

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#562748

On 3/15/2016 6:16 PM, Sam Wormley wrote:
> Mathematician pair find prime numbers aren't as random as thought
>> http://phys.org/news/2016-03-mathematician-pair-prime-random-thought.html
>
>> (Phys.org)—A pair of mathematicians with Stanford University has
>> found that the distribution of the last digit of prime numbers are
>> not as random as has been thought, which suggests prime's themselves
>> are not. In their paper uploaded to the preprint server arXiv, Robert
>> Lemke Oliver and Kannan Soundararajan describe their study of the
>> last digit in prime numbers, how they found it to be less than
>> random, and what they believe is a possible explanation for their
>> findings.
>>
>
>
> Unexpected biases in the distribution of consecutive primes
>> http://arxiv.org/abs/1603.03720
>
>> While the sequence of primes is very well distributed in the reduced
>> residue classes (mod q), the distribution of pairs of consecutive
>> primes among the permissible ϕ(q)2 pairs of reduced residue classes
>> (mod q) is surprisingly erratic. This paper proposes a conjectural
>> explanation for this phenomenon, based on the Hardy-Littlewood
>> conjectures. The conjectures are then compared to numerical data, and
>> the observed fit is very good.
>

Hi,

I think this might have a simple explanation, for each prime n,
with corresponding prime density (based on magnitude of n),
there will be a point x, where the next prime is statistically
most likely to occur, and for all odd numbers ending in 1,3,7,9
around the point x and greater than n, they have a statistical
likelihood of being the next prime based on their distance from x.

So if for every prime that calculation is done, maybe the statistics
will even out and show that consecutive primes ending in 7 occur
less frequently etc, since there are other possible prime closer to
x than 7's are.

Thoughts?

cheers,
Jamie

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#562930

odd binaries end in one (1

> most likely to occur, and for all odd numbers ending in 1,3,7,9
> around the point x and greater than n, they have a statistical
> likelihood of being the next prime based on their distance from x.
> 
> So if for every prime that calculation is done, maybe the statistics
> will even out and show that consecutive primes ending in 7 occur
> less frequently etc, since there are other possible prime closer to
> x than 7's are.
> 
> Thoughts?
> 
> cheers,
> Jamie

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#562958

On 03/15/2016 09:16 PM, Sam Wormley wrote:
> Mathematician pair find prime numbers aren't as random as thought
>> http://phys.org/news/2016-03-mathematician-pair-prime-random-thought.html
> 
>> (Phys.org)—A pair of mathematicians with Stanford University has
>> found that the distribution of the last digit of prime numbers are
>> not as random as has been thought, which suggests prime's themselves
>> are not. In their paper uploaded to the preprint server arXiv, Robert
>> Lemke Oliver and Kannan Soundararajan describe their study of the
>> last digit in prime numbers, how they found it to be less than
>> random, and what they believe is a possible explanation for their
>> findings.
>>
> 
> 
> Unexpected biases in the distribution of consecutive primes
>> http://arxiv.org/abs/1603.03720
> 
>> While the sequence of primes is very well distributed in the reduced
>> residue classes (mod q), the distribution of pairs of consecutive
>> primes among the permissible ϕ(q)2 pairs of reduced residue classes
>> (mod q) is surprisingly erratic. This paper proposes a conjectural
>> explanation for this phenomenon, based on the Hardy-Littlewood
>> conjectures. The conjectures are then compared to numerical data, and
>> the observed fit is very good.
> 

I've looked at primes modulo 10. When the last prime is 9 modulo 10,
I've counted instances of the next prime being 1 modulo 10, and
9 modulo 10, with sequences "9 1" mod 10 counted by
c91 and with sequences "9 9" mod 10 being counted by c99 .

Where both primes are below 1000 (resp. 10^6 and so on),
I get with PARI/gp:

up to 1000:
c91=14 ,  c99=5

up to 10^6:
c91=6948 ,  c99=3155

up to 10^8:
c91=476348 , c99=254684

up to 10^9:
c91= 4092457  , c99= 2328896


up to 10^10:
c91= 35860558 , c99= 21424245 .

David Bernier


? c99 = 0; c91 = 0; lastp=7; forprime(q = 8, 1000, rc=q%10; rl=lastp%10;
if(abs(rl-9)<1, if(abs(rc-9)<1, c99= c99+1); if(abs(rc-1)<1, c91 =
c91+1)); lastp = q); print(c91,"   ",c99);
14   5

? c99 = 0; c91 = 0; lastp=7; forprime(q = 8, 10^6, rc=q%10; rl=lastp%10;
if(abs(rl-9)<1, if(abs(rc-9)<1, c99= c99+1); if(abs(rc-1)<1, c91 =
c91+1)); lastp = q); print(c91,"   ",c99);
6948   3155

? c99 = 0; c91 = 0; lastp=7; forprime(q = 8, 10^8, rc=q%10; rl=lastp%10;
if(abs(rl-9)<1, if(abs(rc-9)<1, c99= c99+1); if(abs(rc-1)<1, c91 =
c91+1)); lastp = q); print(c91,"   ",c99);
476348   254684

? c99 = 0; c91 = 0; lastp=7; forprime(q = 8, 10^9, rc=q%10; rl=lastp%10;
if(abs(rl-9)<1, if(abs(rc-9)<1, c99= c99+1); if(abs(rc-1)<1, c91 =
c91+1)); lastp = q); print(c91,"   ",c99);
4092457   2328896

? c99 = 0; c91 = 0; lastp=7; forprime(q = 8, 10^10, rc=q%10;
rl=lastp%10; if(abs(rl-9)<1, if(abs(rc-9)<1, c99= c99+1);
if(abs(rc-1)<1, c91 = c91+1)); lastp = q); print(c91,"   ",c99);
35860558   21424245


-- 
pub   4096R/41C769D6 2014-11-04
uid                  David Bernier (doubledeckerpot5)
<david250@videotron.ca>

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#563030

David Bernier wrote:
> 
> On 03/15/2016 09:16 PM, Sam Wormley wrote:
> > Mathematician pair find prime numbers aren't as random as thought
> >> http://phys.org/news/2016-03-mathematician-pair-prime-random-thought.html
> >
> >> (Phys.org)—A pair of mathematicians with Stanford University has
> >> found that the distribution of the last digit of prime numbers are
> >> not as random as has been thought, which suggests prime's themselves
> >> are not. In their paper uploaded to the preprint server arXiv, Robert
> >> Lemke Oliver and Kannan Soundararajan describe their study of the
> >> last digit in prime numbers, how they found it to be less than
> >> random, and what they believe is a possible explanation for their
> >> findings.
> >>
> >
> >
> > Unexpected biases in the distribution of consecutive primes
> >> http://arxiv.org/abs/1603.03720
> >
> >> While the sequence of primes is very well distributed in the reduced
> >> residue classes (mod q), the distribution of pairs of consecutive
> >> primes among the permissible Ï•(q)2 pairs of reduced residue classes
> >> (mod q) is surprisingly erratic. This paper proposes a conjectural
> >> explanation for this phenomenon, based on the Hardy-Littlewood
> >> conjectures. The conjectures are then compared to numerical data, and
> >> the observed fit is very good.
> >
> 
> I've looked at primes modulo 10. When the last prime is 9 modulo 10,
> I've counted instances of the next prime being 1 modulo 10, and
> 9 modulo 10, with sequences "9 1" mod 10 counted by
> c91 and with sequences "9 9" mod 10 being counted by c99 .
> 
> Where both primes are below 1000 (resp. 10^6 and so on),
> I get with PARI/gp:
> 
> up to 1000:
> c91=14 ,  c99=5
> 
> up to 10^6:
> c91=6948 ,  c99=3155
> 
> up to 10^8:
> c91=476348 , c99=254684
> 
> up to 10^9:
> c91= 4092457  , c99= 2328896
> 
> up to 10^10:
> c91= 35860558 , c99= 21424245 .
> 
> David Bernier
> 
> ? c99 = 0; c91 = 0; lastp=7; forprime(q = 8, 1000, rc=q%10; rl=lastp%10;
> if(abs(rl-9)<1, if(abs(rc-9)<1, c99= c99+1); if(abs(rc-1)<1, c91 =
> c91+1)); lastp = q); print(c91,"   ",c99);
> 14   5
> 
> ? c99 = 0; c91 = 0; lastp=7; forprime(q = 8, 10^6, rc=q%10; rl=lastp%10;
> if(abs(rl-9)<1, if(abs(rc-9)<1, c99= c99+1); if(abs(rc-1)<1, c91 =
> c91+1)); lastp = q); print(c91,"   ",c99);
> 6948   3155
> 
> ? c99 = 0; c91 = 0; lastp=7; forprime(q = 8, 10^8, rc=q%10; rl=lastp%10;
> if(abs(rl-9)<1, if(abs(rc-9)<1, c99= c99+1); if(abs(rc-1)<1, c91 =
> c91+1)); lastp = q); print(c91,"   ",c99);
> 476348   254684
> 
> ? c99 = 0; c91 = 0; lastp=7; forprime(q = 8, 10^9, rc=q%10; rl=lastp%10;
> if(abs(rl-9)<1, if(abs(rc-9)<1, c99= c99+1); if(abs(rc-1)<1, c91 =
> c91+1)); lastp = q); print(c91,"   ",c99);
> 4092457   2328896
> 
> ? c99 = 0; c91 = 0; lastp=7; forprime(q = 8, 10^10, rc=q%10;
> rl=lastp%10; if(abs(rl-9)<1, if(abs(rc-9)<1, c99= c99+1);
> if(abs(rc-1)<1, c91 = c91+1)); lastp = q); print(c91,"   ",c99);
> 35860558   21424245
> 
> --
> pub   4096R/41C769D6 2014-11-04
> uid                  David Bernier (doubledeckerpot5)
> <david250@videotron.ca>


I always knew there is no such thing as random...but where do patterns
come from?

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