[seqfan] Re: Prime is not random

Olivier Gerard olivier.gerard at gmail.com
Mon Jun 12 06:11:14 CEST 2017


Dear Yasutoshi,


You write

"Because if Prime behaves randomly then the probability of 0 and 2 must be
the same"

No, this does not follow.
Remember also that random does not imply equidistributed.
You

No one serious says that primes are strictly random
in every aspect and every sense of the word.

If you want to test an hypothesis, you have to express it precisely,
preferably in the form of an explicit formula.

Anyway, here are the results of your function for the 100 000 first primes

Count of isolated values
{{1, 1}, {2, 37633}, {0, 62366}}

Count of successive values
{{{1, 2}, 1}, {{2, 0}, 17106}, {{0, 0}, 45260}, {{0, 2}, 17106}, {{2, 2},
20526}}

Count of truples
{{{1, 2, 0}, 1}, {{2, 0, 0},
  12992}, {{0, 0, 0}, 32268}, {{0, 0, 2}, 12992}, {{0, 2, 2},
  10763}, {{2, 2, 0}, 10762}, {{2, 2, 2}, 9763}, {{2, 0, 2},
  4114}, {{0, 2, 0}, 6343}}





On Mon, Jun 12, 2017 at 5:40 AM, <zbi74583.boat at orange.zero.jp> wrote:

>     Hi  Seqfans
>
>     a(n)=Prime(n)+Prime(n+M_3(Prime(n)))  Mod 4
>     Where if m=1 Mod 3 then M_3(m)=-1
>               if m=2 Mod 3 then M_3(m)= 1
>
>     a(n) : 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
> 2, 2,
> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
>     If Prime(n) and Prime(n+1) are twin then a(n)=0 and a(n+1)=0
>     I think it represents the Non Randomness of Prime
>     Because if Prime behaves randomly then the probability of 0 and 2 must
> be
> the same
>
>     b(n)=Prime(n)+Prime(n-M_3(Prime(n)))  Mod 4
>     b(n) : 0, 2, 2, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 0, 0, 0, 2, 2, 0, 2, 2,
> 0, 2,
> 2
>
>     Could anyone compute more term  ?
>
>
>
>     Yasutoshi
>
>
>
> --
> Seqfan Mailing list - http://list.seqfan.eu/
>



More information about the SeqFan mailing list