[seqfan] Re: Prime is not random

[Peter Munn]

Hi.

I think this type of statistic can be affected by the primes being
relatively close together, and in such a case it might be worth examining
the result of the function on the 101-digit (probable) primes from
A049014.

In this particular case a(n) depends on the sum of a prime and its nearest
prime in a specified direction.  In this direction the nearest numbers
that might be prime by modulo 30 arithmetic differ by 2 or 6 and when
either of these numbers is prime the result is 0.

Regards,

Peter

On Mon, 12 June, 2017 4:40 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
>
>
>
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>