2016年10月2日日曜日

161002(2)

Ruby


y^2 = x^3 - k

p を法とする楕円曲線上の点の数を求めてみた。

require 'prime'

def A(a3, a2, a4, a6, n)
  ary = []
  Prime.take(n).each{|p|
    a = Array.new(p, 0)
    (0..p - 1).each{|i| a[(i * i + a3 * i) % p] += 1}
    ary << (0..p - 1).inject(0){|s, i| s + a[(i * i * i + a2 * i * i + a4 * i + a6) % p]}
  }
  ary
end

m = 4
n = 25
ary = []
a = []
(1..m * 64).each{|i|
  j = A(0, 0, 0, -i, n)
  if !ary.include?(j)
    ary << j
    p [i, j]
  else
    a << i
  end
}
p a

n = 200
(1..m).each{|i| p A(0, 0, 0, -i, n) == A(0, 0, 0, -i * 64, n)}

出力結果
[1, [2, 3, 5, 3, 11, 11, 17, 27, 23, 29, 27, 47, 41, 51, 47, 53, 59, 47, 51, 71, 83, 75, 83, 89, 83]]
[2, [2, 3, 5, 6, 11, 18, 17, 26, 23, 29, 27, 48, 41, 35, 47, 53, 59, 60, 62, 71, 80, 96, 83, 89, 116]]
[3, [2, 3, 5, 2, 11, 8, 17, 26, 23, 29, 20, 38, 41, 38, 47, 53, 59, 47, 83, 71, 83, 62, 83, 89, 116]]
[4, [2, 3, 5, 12, 11, 20, 17, 18, 23, 29, 27, 38, 41, 51, 47, 53, 59, 74, 78, 71, 56, 66, 83, 89, 92]]
[5, [2, 3, 5, 8, 11, 15, 17, 12, 23, 29, 24, 36, 41, 38, 47, 53, 59, 62, 83, 71, 90, 66, 83, 89, 78]]
[6, [2, 3, 5, 11, 11, 6, 17, 18, 23, 29, 20, 27, 41, 48, 47, 53, 59, 60, 72, 71, 80, 92, 83, 89, 92]]
[7, [2, 3, 5, 7, 11, 6, 17, 27, 23, 29, 42, 38, 41, 56, 47, 53, 59, 60, 56, 71, 63, 92, 83, 89, 78]]
[8, [2, 3, 5, 3, 11, 15, 17, 11, 23, 29, 27, 27, 41, 35, 47, 53, 59, 75, 83, 71, 83, 75, 83, 89, 83]]
[9, [2, 3, 5, 6, 11, 20, 17, 18, 23, 29, 24, 26, 41, 30, 47, 53, 59, 47, 51, 71, 83, 66, 83, 89, 92]]
[10, [2, 3, 5, 2, 11, 8, 17, 20, 23, 29, 24, 47, 41, 48, 47, 53, 59, 48, 72, 71, 63, 75, 83, 89, 102]]
[11, [2, 3, 5, 12, 11, 18, 17, 27, 23, 29, 38, 47, 41, 51, 47, 53, 59, 75, 56, 71, 90, 66, 83, 89, 92]]
[12, [2, 3, 5, 8, 11, 11, 17, 11, 23, 29, 20, 26, 41, 38, 47, 53, 59, 74, 56, 71, 56, 83, 83, 89, 83]]
[13, [2, 3, 5, 11, 11, 13, 17, 20, 23, 29, 38, 36, 41, 30, 47, 53, 59, 62, 62, 71, 66, 96, 83, 89, 78]]
[14, [2, 3, 5, 7, 11, 11, 17, 26, 23, 29, 42, 27, 41, 30, 47, 53, 59, 74, 51, 71, 66, 83, 83, 89, 102]]
[15, [2, 3, 5, 3, 11, 18, 17, 20, 23, 29, 35, 48, 41, 30, 47, 53, 59, 62, 51, 71, 90, 83, 83, 89, 102]]
[16, [2, 3, 5, 6, 11, 8, 17, 12, 23, 29, 27, 26, 41, 51, 47, 53, 59, 62, 72, 71, 80, 96, 83, 89, 116]]
[17, [2, 3, 5, 2, 11, 20, 17, 12, 23, 29, 20, 48, 41, 30, 47, 53, 59, 48, 72, 71, 63, 83, 83, 89, 102]]
[18, [2, 3, 5, 12, 11, 15, 17, 11, 23, 29, 24, 36, 41, 56, 47, 53, 59, 60, 62, 71, 80, 75, 83, 89, 83]]
[19, [2, 3, 5, 8, 11, 6, 17, 19, 23, 29, 42, 36, 41, 38, 47, 53, 59, 74, 72, 71, 80, 66, 83, 89, 111]]
[20, [2, 3, 5, 11, 11, 6, 17, 27, 23, 29, 24, 48, 41, 38, 47, 53, 59, 47, 56, 71, 66, 96, 83, 89, 111]]
[21, [2, 3, 5, 7, 11, 15, 17, 26, 23, 29, 38, 26, 41, 51, 47, 53, 59, 60, 78, 71, 63, 75, 83, 89, 102]]
[22, [2, 3, 5, 3, 11, 20, 17, 26, 23, 29, 38, 48, 41, 35, 47, 53, 59, 62, 51, 71, 63, 75, 83, 89, 83]]
[23, [2, 3, 5, 6, 11, 8, 17, 18, 23, 29, 35, 27, 41, 48, 47, 53, 59, 75, 72, 71, 56, 66, 83, 89, 102]]
[24, [2, 3, 5, 2, 11, 18, 17, 12, 23, 29, 20, 36, 41, 48, 47, 53, 59, 75, 51, 71, 83, 62, 83, 89, 116]]
[25, [2, 3, 5, 12, 11, 11, 17, 18, 23, 29, 42, 26, 41, 30, 47, 53, 59, 74, 51, 71, 80, 96, 83, 89, 92]]
[26, [2, 3, 5, 8, 11, 13, 17, 27, 23, 29, 38, 47, 41, 56, 47, 53, 59, 48, 78, 71, 90, 66, 83, 89, 102]]
[27, [2, 3, 5, 11, 11, 11, 17, 11, 23, 29, 35, 47, 41, 35, 47, 53, 59, 47, 83, 71, 83, 83, 83, 89, 83]]
[28, [2, 3, 5, 7, 11, 18, 17, 18, 23, 29, 42, 26, 41, 56, 47, 53, 59, 75, 62, 71, 90, 62, 83, 89, 111]]
[29, [2, 3, 5, 3, 11, 8, 17, 20, 23, 29, 35, 27, 41, 56, 47, 53, 59, 48, 78, 71, 66, 92, 83, 89, 78]]
[30, [2, 3, 5, 6, 11, 20, 17, 27, 23, 29, 35, 38, 41, 56, 47, 53, 59, 48, 62, 71, 63, 62, 83, 89, 111]]
[31, [2, 3, 5, 2, 11, 15, 17, 11, 23, 29, 31, 27, 41, 48, 47, 53, 59, 48, 56, 71, 66, 66, 83, 89, 116]]
[32, [2, 3, 5, 12, 11, 6, 17, 20, 23, 29, 27, 36, 41, 35, 47, 53, 59, 48, 56, 71, 56, 66, 83, 89, 92]]
[33, [2, 3, 5, 8, 11, 6, 17, 26, 23, 29, 27, 38, 41, 38, 47, 53, 59, 75, 78, 71, 90, 83, 83, 89, 83]]
[34, [2, 3, 5, 11, 11, 15, 17, 20, 23, 29, 20, 38, 41, 56, 47, 53, 59, 47, 56, 71, 66, 62, 83, 89, 111]]
[35, [2, 3, 5, 7, 11, 20, 17, 12, 23, 29, 27, 48, 41, 51, 47, 53, 59, 48, 78, 71, 56, 62, 83, 89, 92]]
[36, [2, 3, 5, 3, 11, 8, 17, 12, 23, 29, 24, 47, 41, 30, 47, 53, 59, 74, 78, 71, 56, 96, 83, 89, 116]]
[37, [2, 3, 5, 6, 11, 18, 17, 11, 23, 29, 20, 37, 41, 38, 47, 53, 59, 75, 72, 71, 56, 62, 83, 89, 78]]
[38, [2, 3, 5, 2, 11, 11, 17, 19, 23, 29, 42, 47, 41, 48, 47, 53, 59, 75, 56, 71, 56, 75, 83, 89, 78]]
[39, [2, 3, 5, 12, 11, 13, 17, 27, 23, 29, 27, 48, 41, 35, 47, 53, 59, 62, 72, 71, 66, 92, 83, 89, 102]]
[40, [2, 3, 5, 8, 11, 11, 17, 26, 23, 29, 24, 38, 41, 48, 47, 53, 59, 60, 51, 71, 90, 66, 83, 89, 78]]
[41, [2, 3, 5, 11, 11, 18, 17, 26, 23, 29, 24, 38, 41, 51, 47, 53, 59, 47, 56, 71, 56, 83, 83, 89, 78]]
[42, [2, 3, 5, 7, 11, 8, 17, 18, 23, 29, 38, 36, 41, 35, 47, 53, 59, 74, 83, 71, 66, 96, 83, 89, 111]]
[43, [2, 3, 5, 3, 11, 20, 17, 12, 23, 29, 20, 27, 41, 43, 47, 53, 59, 60, 83, 71, 63, 62, 83, 89, 116]]
[44, [2, 3, 5, 6, 11, 15, 17, 18, 23, 29, 38, 38, 41, 51, 47, 53, 59, 48, 62, 71, 66, 96, 83, 89, 116]]
[45, [2, 3, 5, 2, 11, 6, 17, 27, 23, 29, 42, 27, 41, 35, 47, 53, 59, 62, 83, 71, 90, 96, 83, 89, 111]]
[46, [2, 3, 5, 12, 11, 6, 17, 11, 23, 29, 35, 26, 41, 38, 47, 53, 59, 62, 56, 71, 83, 75, 83, 89, 111]]
[47, [2, 3, 5, 8, 11, 15, 17, 18, 23, 29, 27, 47, 41, 51, 47, 53, 59, 74, 78, 71, 90, 92, 83, 89, 83]]
[48, [2, 3, 5, 11, 11, 20, 17, 20, 23, 29, 20, 47, 41, 38, 47, 53, 59, 62, 62, 71, 80, 92, 83, 89, 92]]
[49, [2, 3, 5, 7, 11, 8, 17, 27, 23, 29, 24, 26, 41, 48, 47, 53, 59, 74, 72, 71, 83, 96, 83, 89, 92]]
[50, [2, 3, 5, 3, 11, 18, 17, 11, 23, 29, 42, 36, 41, 56, 47, 53, 59, 75, 62, 71, 56, 66, 83, 89, 83]]
[51, [2, 3, 5, 6, 11, 11, 17, 20, 23, 29, 24, 27, 41, 35, 47, 53, 59, 48, 62, 71, 63, 96, 83, 89, 111]]
[52, [2, 3, 5, 2, 11, 13, 17, 26, 23, 29, 38, 48, 41, 30, 47, 53, 59, 47, 83, 71, 63, 75, 83, 89, 111]]
[53, [2, 3, 5, 12, 11, 11, 17, 20, 23, 29, 38, 26, 41, 48, 47, 53, 59, 75, 83, 71, 66, 92, 83, 89, 116]]
[54, [2, 3, 5, 8, 11, 18, 17, 12, 23, 29, 35, 48, 41, 51, 47, 53, 59, 60, 72, 71, 80, 62, 83, 89, 116]]
[55, [2, 3, 5, 11, 11, 8, 17, 12, 23, 29, 20, 36, 41, 38, 47, 53, 59, 60, 78, 71, 80, 96, 83, 89, 111]]
[56, [2, 3, 5, 7, 11, 20, 17, 11, 23, 29, 42, 36, 41, 30, 47, 53, 59, 62, 78, 71, 63, 92, 83, 89, 78]]
[57, [2, 3, 5, 3, 11, 15, 17, 19, 23, 29, 38, 48, 41, 30, 47, 53, 59, 74, 62, 71, 80, 83, 83, 89, 78]]
[58, [2, 3, 5, 6, 11, 6, 17, 27, 23, 29, 35, 26, 41, 30, 47, 53, 59, 47, 83, 71, 90, 83, 83, 89, 102]]
[59, [2, 3, 5, 2, 11, 6, 17, 26, 23, 29, 42, 48, 41, 51, 47, 53, 59, 60, 51, 71, 66, 62, 83, 89, 78]]
[60, [2, 3, 5, 12, 11, 15, 17, 26, 23, 29, 35, 27, 41, 30, 47, 53, 59, 47, 78, 71, 66, 92, 83, 89, 78]]
[61, [2, 3, 5, 8, 11, 20, 17, 18, 23, 29, 35, 36, 41, 56, 47, 53, 59, 61, 62, 71, 56, 83, 83, 89, 116]]
[62, [2, 3, 5, 11, 11, 8, 17, 12, 23, 29, 31, 26, 41, 38, 47, 53, 59, 47, 51, 71, 90, 75, 83, 89, 92]]
[63, [2, 3, 5, 7, 11, 18, 17, 18, 23, 29, 27, 47, 41, 38, 47, 53, 59, 60, 56, 71, 63, 62, 83, 89, 111]]
[65, [2, 3, 5, 6, 11, 13, 17, 11, 23, 29, 20, 26, 41, 35, 47, 53, 59, 74, 72, 71, 83, 75, 83, 89, 92]]
[66, [2, 3, 5, 2, 11, 11, 17, 18, 23, 29, 27, 27, 41, 48, 47, 53, 59, 62, 83, 71, 63, 62, 83, 89, 116]]
[67, [2, 3, 5, 12, 11, 18, 17, 20, 23, 29, 24, 38, 41, 48, 47, 53, 59, 60, 67, 71, 80, 75, 83, 89, 111]]
[68, [2, 3, 5, 8, 11, 8, 17, 27, 23, 29, 20, 27, 41, 30, 47, 53, 59, 60, 51, 71, 90, 92, 83, 89, 78]]
[69, [2, 3, 5, 11, 11, 20, 17, 11, 23, 29, 42, 36, 41, 56, 47, 53, 59, 75, 62, 71, 56, 83, 83, 89, 111]]
[70, [2, 3, 5, 7, 11, 15, 17, 20, 23, 29, 27, 38, 41, 35, 47, 53, 59, 47, 83, 71, 83, 92, 83, 89, 83]]
[71, [2, 3, 5, 3, 11, 6, 17, 26, 23, 29, 24, 38, 41, 56, 47, 53, 59, 48, 78, 71, 80, 83, 83, 89, 102]]
[72, [2, 3, 5, 6, 11, 6, 17, 20, 23, 29, 24, 48, 41, 56, 47, 53, 59, 75, 83, 71, 83, 66, 83, 89, 92]]
[73, [2, 3, 5, 2, 11, 15, 17, 12, 23, 29, 38, 47, 41, 56, 47, 53, 59, 74, 72, 71, 73, 66, 83, 89, 116]]
[74, [2, 3, 5, 12, 11, 20, 17, 12, 23, 29, 20, 37, 41, 48, 47, 53, 59, 62, 56, 71, 83, 92, 83, 89, 102]]
[75, [2, 3, 5, 8, 11, 8, 17, 11, 23, 29, 38, 47, 41, 35, 47, 53, 59, 74, 83, 71, 80, 92, 83, 89, 83]]
[76, [2, 3, 5, 11, 11, 18, 17, 19, 23, 29, 42, 48, 41, 38, 47, 53, 59, 62, 51, 71, 83, 96, 83, 89, 102]]
[77, [2, 3, 5, 7, 11, 11, 17, 27, 23, 29, 35, 38, 41, 56, 47, 53, 59, 62, 72, 71, 56, 62, 83, 89, 111]]
[78, [2, 3, 5, 3, 11, 13, 17, 26, 23, 29, 27, 38, 41, 51, 47, 53, 59, 48, 56, 71, 90, 83, 83, 89, 111]]
[79, [2, 3, 5, 6, 11, 11, 17, 26, 23, 29, 20, 36, 41, 30, 47, 53, 59, 60, 56, 71, 80, 79, 83, 89, 83]]
[80, [2, 3, 5, 2, 11, 18, 17, 18, 23, 29, 24, 27, 41, 38, 47, 53, 59, 74, 62, 71, 63, 75, 83, 89, 102]]
[81, [2, 3, 5, 12, 11, 8, 17, 12, 23, 29, 42, 38, 41, 48, 47, 53, 59, 47, 51, 71, 83, 96, 83, 89, 116]]
[82, [2, 3, 5, 8, 11, 20, 17, 18, 23, 29, 24, 27, 41, 35, 47, 53, 59, 60, 51, 71, 83, 62, 83, 89, 102]]
[83, [2, 3, 5, 11, 11, 15, 17, 27, 23, 29, 38, 26, 41, 48, 47, 53, 59, 62, 72, 71, 63, 66, 83, 89, 102]]
[84, [2, 3, 5, 7, 11, 6, 17, 11, 23, 29, 38, 47, 41, 51, 47, 53, 59, 75, 72, 71, 90, 66, 83, 89, 78]]
[85, [2, 3, 5, 3, 11, 6, 17, 18, 23, 29, 35, 47, 41, 35, 47, 53, 59, 75, 62, 71, 56, 92, 83, 89, 83]]
[86, [2, 3, 5, 6, 11, 15, 17, 20, 23, 29, 20, 26, 41, 43, 47, 53, 59, 74, 72, 71, 66, 92, 83, 89, 92]]
[87, [2, 3, 5, 2, 11, 20, 17, 27, 23, 29, 42, 36, 41, 51, 47, 53, 59, 48, 56, 71, 66, 75, 83, 89, 102]]
[88, [2, 3, 5, 12, 11, 8, 17, 11, 23, 29, 38, 27, 41, 35, 47, 53, 59, 47, 78, 71, 90, 66, 83, 89, 92]]
[89, [2, 3, 5, 8, 11, 18, 17, 20, 23, 29, 35, 48, 41, 38, 47, 53, 59, 75, 51, 71, 80, 75, 83, 89, 83]]
[90, [2, 3, 5, 11, 11, 11, 17, 26, 23, 29, 42, 26, 41, 51, 47, 53, 59, 48, 72, 71, 63, 66, 83, 89, 78]]
[91, [2, 3, 5, 7, 11, 13, 17, 20, 23, 29, 35, 48, 41, 38, 47, 53, 59, 48, 51, 71, 80, 83, 83, 89, 92]]
[92, [2, 3, 5, 3, 11, 11, 17, 12, 23, 29, 35, 36, 41, 48, 47, 53, 59, 48, 51, 71, 80, 96, 83, 89, 78]]
[93, [2, 3, 5, 6, 11, 18, 17, 12, 23, 29, 31, 36, 41, 56, 47, 53, 59, 48, 78, 71, 66, 83, 83, 89, 92]]
[94, [2, 3, 5, 2, 11, 8, 17, 11, 23, 29, 27, 48, 41, 35, 47, 53, 59, 75, 83, 71, 63, 83, 83, 89, 116]]
[95, [2, 3, 5, 12, 11, 20, 17, 19, 23, 29, 27, 26, 41, 30, 47, 53, 59, 47, 62, 71, 63, 96, 83, 89, 116]]
[96, [2, 3, 5, 8, 11, 15, 17, 27, 23, 29, 20, 48, 41, 48, 47, 53, 59, 48, 78, 71, 56, 83, 83, 89, 83]]
[97, [2, 3, 5, 11, 11, 6, 17, 26, 23, 29, 27, 27, 41, 51, 47, 53, 59, 74, 62, 71, 83, 75, 83, 89, 97]]
[98, [2, 3, 5, 7, 11, 6, 17, 26, 23, 29, 24, 36, 41, 38, 47, 53, 59, 75, 56, 71, 80, 66, 83, 89, 83]]
[99, [2, 3, 5, 3, 11, 15, 17, 18, 23, 29, 20, 26, 41, 30, 47, 53, 59, 75, 56, 71, 90, 96, 83, 89, 116]]
[100, [2, 3, 5, 6, 11, 20, 17, 12, 23, 29, 42, 47, 41, 30, 47, 53, 59, 62, 78, 71, 83, 75, 83, 89, 116]]
[101, [2, 3, 5, 2, 11, 8, 17, 18, 23, 29, 27, 47, 41, 30, 47, 53, 59, 60, 56, 71, 90, 75, 83, 89, 92]]
[102, [2, 3, 5, 12, 11, 18, 17, 27, 23, 29, 24, 26, 41, 51, 47, 53, 59, 47, 78, 71, 66, 66, 83, 89, 78]]
[103, [2, 3, 5, 8, 11, 11, 17, 11, 23, 29, 24, 27, 41, 30, 47, 53, 59, 74, 78, 71, 63, 62, 83, 89, 92]]
[104, [2, 3, 5, 11, 11, 13, 17, 18, 23, 29, 38, 38, 41, 56, 47, 53, 59, 60, 72, 71, 66, 96, 83, 89, 78]]
[105, [2, 3, 5, 7, 11, 11, 17, 20, 23, 29, 20, 27, 41, 38, 47, 53, 59, 48, 56, 71, 56, 66, 83, 89, 83]]
[106, [2, 3, 5, 3, 11, 18, 17, 27, 23, 29, 38, 36, 41, 38, 47, 53, 59, 62, 72, 71, 90, 83, 83, 89, 92]]
[107, [2, 3, 5, 6, 11, 8, 17, 11, 23, 29, 42, 38, 41, 51, 47, 53, 59, 62, 51, 71, 66, 62, 83, 89, 102]]
[108, [2, 3, 5, 2, 11, 20, 17, 20, 23, 29, 35, 38, 41, 35, 47, 53, 59, 74, 56, 71, 56, 92, 83, 89, 92]]
[109, [2, 3, 5, 12, 11, 15, 17, 26, 23, 29, 27, 48, 41, 48, 47, 53, 59, 62, 83, 71, 56, 62, 83, 89, 83]]
[110, [2, 3, 5, 8, 11, 6, 17, 20, 23, 29, 20, 47, 41, 48, 47, 53, 59, 74, 83, 71, 56, 66, 83, 89, 78]]
[111, [2, 3, 5, 11, 11, 6, 17, 12, 23, 29, 24, 37, 41, 30, 47, 53, 59, 75, 62, 71, 56, 66, 83, 89, 102]]
[112, [2, 3, 5, 7, 11, 15, 17, 12, 23, 29, 42, 47, 41, 56, 47, 53, 59, 48, 83, 71, 66, 83, 83, 89, 102]]
[113, [2, 3, 5, 3, 11, 20, 17, 11, 23, 29, 24, 48, 41, 35, 47, 53, 59, 47, 56, 71, 90, 62, 83, 89, 116]]
[114, [2, 3, 5, 6, 11, 8, 17, 19, 23, 29, 38, 38, 41, 56, 47, 53, 59, 75, 78, 71, 56, 62, 83, 89, 102]]
[115, [2, 3, 5, 2, 11, 18, 17, 27, 23, 29, 38, 38, 41, 56, 47, 53, 59, 60, 62, 71, 66, 96, 83, 89, 83]]
[116, [2, 3, 5, 12, 11, 11, 17, 26, 23, 29, 35, 36, 41, 56, 47, 53, 59, 60, 72, 71, 63, 62, 83, 89, 111]]
[117, [2, 3, 5, 8, 11, 13, 17, 26, 23, 29, 20, 27, 41, 48, 47, 53, 59, 62, 62, 71, 66, 75, 83, 89, 111]]
[118, [2, 3, 5, 11, 11, 11, 17, 18, 23, 29, 42, 38, 41, 35, 47, 53, 59, 74, 62, 71, 90, 92, 83, 89, 102]]
[119, [2, 3, 5, 7, 11, 18, 17, 12, 23, 29, 38, 27, 41, 38, 47, 53, 59, 47, 83, 71, 83, 66, 83, 89, 83]]
[120, [2, 3, 5, 3, 11, 8, 17, 18, 23, 29, 35, 26, 41, 56, 47, 53, 59, 60, 83, 71, 90, 83, 83, 89, 102]]
[121, [2, 3, 5, 6, 11, 20, 17, 27, 23, 29, 42, 47, 41, 51, 47, 53, 59, 47, 72, 71, 80, 96, 83, 89, 116]]
[122, [2, 3, 5, 2, 11, 15, 17, 11, 23, 29, 35, 47, 41, 30, 47, 53, 59, 61, 78, 71, 83, 62, 83, 89, 92]]
[123, [2, 3, 5, 12, 11, 6, 17, 18, 23, 29, 35, 26, 41, 38, 47, 53, 59, 47, 78, 71, 56, 96, 83, 89, 102]]
[124, [2, 3, 5, 8, 11, 6, 17, 20, 23, 29, 31, 36, 41, 48, 47, 53, 59, 60, 62, 71, 63, 96, 83, 89, 83]]
[125, [2, 3, 5, 11, 11, 15, 17, 27, 23, 29, 27, 27, 41, 35, 47, 53, 59, 47, 83, 71, 63, 75, 83, 89, 111]]
[126, [2, 3, 5, 7, 11, 20, 17, 11, 23, 29, 27, 48, 41, 48, 47, 53, 59, 74, 51, 71, 66, 92, 83, 89, 78]]
[127, [2, 3, 5, 3, 11, 8, 17, 20, 23, 29, 20, 26, 41, 51, 47, 53, 59, 62, 78, 71, 80, 92, 83, 89, 111]]
[129, [2, 3, 5, 2, 11, 11, 17, 20, 23, 29, 24, 36, 41, 43, 47, 53, 59, 60, 51, 71, 63, 66, 83, 89, 92]]
[130, [2, 3, 5, 12, 11, 13, 17, 12, 23, 29, 20, 36, 41, 51, 47, 53, 59, 75, 56, 71, 80, 96, 83, 89, 83]]
[131, [2, 3, 5, 8, 11, 11, 17, 12, 23, 29, 42, 48, 41, 35, 47, 53, 59, 47, 51, 71, 90, 75, 83, 89, 111]]
[132, [2, 3, 5, 11, 11, 18, 17, 11, 23, 29, 27, 26, 41, 38, 47, 53, 59, 48, 72, 71, 66, 92, 83, 89, 92]]
[133, [2, 3, 5, 7, 11, 8, 17, 19, 23, 29, 24, 48, 41, 51, 47, 53, 59, 75, 83, 71, 66, 62, 83, 89, 116]]
[134, [2, 3, 5, 3, 11, 20, 17, 27, 23, 29, 24, 27, 41, 38, 47, 53, 59, 74, 67, 71, 56, 96, 83, 89, 78]]
[135, [2, 3, 5, 6, 11, 15, 17, 26, 23, 29, 38, 36, 41, 48, 47, 53, 59, 62, 51, 71, 90, 92, 83, 89, 78]]
[136, [2, 3, 5, 2, 11, 6, 17, 26, 23, 29, 20, 26, 41, 56, 47, 53, 59, 74, 62, 71, 63, 83, 83, 89, 102]]
[137, [2, 3, 5, 12, 11, 6, 17, 18, 23, 29, 38, 47, 41, 35, 47, 53, 59, 62, 83, 71, 83, 83, 83, 89, 78]]
[138, [2, 3, 5, 8, 11, 15, 17, 12, 23, 29, 42, 47, 41, 30, 47, 53, 59, 62, 78, 71, 83, 62, 83, 89, 78]]
[139, [2, 3, 5, 11, 11, 20, 17, 18, 23, 29, 35, 26, 41, 48, 47, 53, 59, 48, 83, 71, 63, 92, 83, 89, 111]]
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