8桁表示で素数日や連続素数日を探す ref: http://qiita.com/qube81/items/e681c4abd28eebe9bbad

file0.txt

require 'prime'
require 'date'

puts [*Date.new(2015, 1, 1).upto(Date.new(2015, 12, 31))].flat_map{|d|
    Prime.prime?(d.strftime('%Y%m%d').to_i) ? [d.to_s] : []
}

file1.txt

2015-01-11
2015-01-31
2015-02-27
2015-03-03
2015-03-27
2015-04-11
2015-05-13
2015-08-21
2015-10-11
2015-10-31
2015-11-27
2015-12-21
2015-12-27

file2.txt

require 'prime'
require 'date'

[*Date.new(2015, 1, 1).upto(Date.new(2020, 12, 31))].flat_map{|d|
    Prime.prime?(d.strftime('%Y%m%d').to_i) ? [d] : []
}.each_cons(2) {|d1, d2|
    puts d1, d2, "\n" if (d2-d1).to_i == 2
}

file3.txt

2016-04-01
2016-04-03

2016-10-19
2016-10-21

2017-03-01
2017-03-03

2017-09-01
2017-09-03

2019-02-27
2019-03-01

2020-01-09
2020-01-11

2020-01-21
2020-01-23

2020-07-21
2020-07-23

file4.txt

require 'prime'
require 'date'

[*Date.new(2015, 1, 1).upto(Date.new(2100, 12, 31))].flat_map{|d|
    Prime.prime?(d.strftime('%Y%m%d').to_i) ? [d] : []
}.each_cons(3) {|d1, d2, d3|
    if (d2-d1).to_i == 2 && (d3-d2).to_i == 2
        puts d1, d2, d3, "\n"
    end
}

file5.txt

2085-06-29
2085-07-01
2085-07-03

2087-04-29
2087-05-01
2087-05-03

file6.txt

require 'prime'
require 'date'

[*Date.new(2015, 1, 1).upto(Date.new(2020, 12, 31))].flat_map{|d|
    Prime.prime?(d.strftime('%Y%m%d').to_i) ? [d] : []
}.each_cons(2) {|d1, d2|
    puts d1, d2, "\n" if (d2-d1).to_i == 1
}

file7.txt

2017-08-31
2017-09-01

2018-07-31
2018-08-01