160317

Ruby

Unexpected biases in the distribution of consecutive primes(1)

http://arxiv.org/pdf/1603.03720v2.pdf
今話題のプレプリントの内容について、自分でも実験してみた。
第10^8 + 3項まででどのような分布になるか調べてみた。

require 'prime'

h = {
  [2, 3] => 0,
  [3, 5] => 0,
  [5, 7] => 0,

  [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 + 3).to_a
(1..N + 3).each{|i| h[[ary[i - 1] % 10, ary[i] % 10]] += 1}
p h

出力結果
{[2, 3]=>1, [3, 5]=>1, [5, 7]=>1, [1, 1]=>4623042, [1, 3]=>7429438, [1, 7]=>7504612, [1, 9]=>5442345, [3, 1]=>6010982, [3, 3]=>4442561, [3, 7]=>7043695, [3, 9]=>7502896, [7, 1]=>6373982, [7, 3]=>6755195, [7, 7]=>4439355, [7, 9]=>7431870, [9, 1]=>7991431, [9, 3]=>6372941, [9, 7]=>6012739, [9, 9]=>4622916}