> For the complete documentation index, see [llms.txt](https://trizen.gitbook.io/sidef-lang/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://trizen.gitbook.io/sidef-lang/programming_tasks/d/de_polignac_numbers.md).

# De Polignac numbers

```ruby
var polignacs = (1..Inf -> by(2).lazy.grep {|n|
    RangeNum(n.ilog2, 0, -1).none {|k| n - (1<<k) -> is_prime }
})

with (50) {|n|
    say ("first #{n} de Polignac numbers:")
    polignacs.first(n).slices(10).each{|s| say("%5d"*s.len % s...) }
}

say ''; [1000, 10000].each{|n|
    say "#{n}th de Polignac number: #{polignacs.nth(n)}"
}
```

#### Output:

```
first 50 de Polignac numbers:
    1  127  149  251  331  337  373  509  599  701
  757  809  877  905  907  959  977  997 1019 1087
 1199 1207 1211 1243 1259 1271 1477 1529 1541 1549
 1589 1597 1619 1649 1657 1719 1759 1777 1783 1807
 1829 1859 1867 1927 1969 1973 1985 2171 2203 2213

1000th de Polignac number: 31941
10000th de Polignac number: 273421
```


---

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