160318

Ruby

Unexpected biases in the distribution of consecutive primes(2)

2, 3, 5, 7 より大きな素数を小さい順に10^8 個とってきたら、
http://arxiv.org/pdf/1603.03720v2.pdf
に載っている分布に一致した。

require 'prime'

h = {
  [1, 1] => 0,
  [1, 3] => 0,
  [1, 7] => 0,
  [1, 9] => 0,
  [3, 1] => 0,
  [3, 3] => 0,
  [3, 7] => 0,
  [3, 9] => 0,
  [7, 1] => 0,
  [7, 3] => 0,
  [7, 7] => 0,
  [7, 9] => 0,
  [9, 1] => 0,
  [9, 3] => 0,
  [9, 7] => 0,
  [9, 9] => 0
}

N = 10 ** 8
ary = Prime.each.take(N + 1 + 4).to_a - [2, 3, 5, 7]
(1..N).each{|i| h[[ary[i - 1] % 10, ary[i] % 10]] += 1}
p h

出力結果
{[1, 1]=>4623042, [1, 3]=>7429438, [1, 7]=>7504612, [1, 9]=>5442345, [3, 1]=>6010982, [3, 3]=>4442562, [3, 7]=>7043695, [3, 9]=>7502896, [7, 1]=>6373981, [7, 3]=>6755195, [7, 7]=>4439355, [7, 9]=>7431870, [9, 1]=>7991431, [9, 3]=>6372941, [9, 7]=>6012739, [9, 9]=>4622916}