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

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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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Thread

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

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