Re: About random, primes and statistics

Concerning Prime[N] modulo 3

I strongly suggest to you, primes split
evenly between
having a residue of 1 and 2 modulo 3.

I checked to 2^22 and it seems to be so.

the sequence

{of Prime[N] modulo 3}

is
2, 1, 2, 1, 2, 1, 2, 2, 1, 1, 2, 1, 2, 2, 2, 1, 1, 2,
1, 1, 2, 2, 1

if 1
tends to be followed by 2 and 2 by 1...

I looked at the four possibilities
p(1->1)
p(1->2)
p(2->1)
p(2->2)

This is graphed as a function of N at
http://physics.technion.ac.il/~rutman/images/primes_mod3_remainders.jpg
{note x-axis off by 2, namely final value is at x=22=log2(N) }
It has an interesting structure. Note bump at N=2^12.
Also values p(1->2) and p(2->1) seem to converge to 0.2766 while values values p(1->1) and p(2->2) converge to 0.2233. Or do they really converge at very large N to 0.25 each? Its very slow convergence if so.
.

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