# Wolstenholme numbers

```ruby
say "Wolstenholme numbers:"

for n in (1..20) {
    say ("#{'%5s'%n}: ", sum(1..n, {|k| 1/k**2 }).nu)
}

for n in (500, 1000, 2500, 5000, 10000) {
    var w = Str(sum(1..n, {|k| 1/k**2 }).nu)
    say ("#{'%5s'%n}: ", w.first(20), '...', w.last(20), " (#{w.len} digits)")
}

say "\nPrime Wolstenholme numbers:"

Enumerator({|callback|
    var w = 0
    for k in (1..Inf) {
        w += 1/k**2
        if (w.nu.is_prime) {
            callback([k, w.nu])
        }
    }
}).first(15).each_2d {|n,p|
    var w = Str(p)
    if (w.len > 50) {
        w = join('', w.first(20), '...', w.last(20), " (#{w.len} digits)")
    }
    say ("#{'%5s'%n}: ", w)
}
```

#### Output:

```
Wolstenholme numbers:
    1: 1
    2: 5
    3: 49
    4: 205
    5: 5269
    6: 5369
    7: 266681
    8: 1077749
    9: 9778141
   10: 1968329
   11: 239437889
   12: 240505109
   13: 40799043101
   14: 40931552621
   15: 205234915681
   16: 822968714749
   17: 238357395880861
   18: 238820721143261
   19: 86364397717734821
   20: 17299975731542641
  500: 40989667509417020364...48084984597965892703 (434 digits)
 1000: 83545938483149689478...99094240207812766449 (866 digits)
 2500: 64537911900230612090...12785535902976933153 (2164 digits)
 5000: 34472086597488537716...22525144829082590451 (4340 digits)
10000: 54714423173933343999...49175649667700005717 (8693 digits)

Prime Wolstenholme numbers:
    2: 5
    7: 266681
   13: 40799043101
   19: 86364397717734821
  121: 36190908596780862323...79995976006474252029 (104 digits)
  188: 33427988094524601237...48446489305085140033 (156 digits)
  252: 22812704758392002353...84405125167217413149 (218 digits)
  368: 28347687473208792918...45794572911130248059 (318 digits)
  605: 78440559440644426017...30422337523878698419 (520 digits)
  745: 22706893975121925531...02173859396183964989 (649 digits)
 1085: 27310394808585898968...86311385662644388271 (935 digits)
 1127: 13001072736642048751...08635832246554146071 (984 digits)
 1406: 15086863305391456002...05367804007944918693 (1202 digits)
 1743: 23541935187269979100...02324742766220468879 (1518 digits)
 1774: 40306783143871607599...58901192511859288941 (1539 digits)
```


---

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