Smarandache-Wellin primes: Difference between revisions

=={{header|Nim}}==

{{libheader|Nim-Integers}}

<syntaxhighlight lang="Nim">import std/[bitops, math, strformat, strutils, sugar, tables]

import integers

const N = 12_000

let primes = @[2] & collect(for n in countup(3, N, 2):

if n.isPrime: n)

func compressed(str: string; size: int): string =

## Return a compressed value for long strings of digits.

if str.len <= 2 * size: str

else: &"{str[0..<size]}...{str[^size..^1]} ({str.len} digits)"

iterator swNumbers(): tuple[value: Integer; lastPrime: int] =

## Yield the SW-Numbers and the last prime added.

var swString = ""

for p in primes:

swString.addInt p

yield (newInteger(swString), p)

iterator derivedSwNumbers(): Integer =

## Yield the derived SW-Numbers.

for (n, _) in swNumbers():

var dSwString = ""

let counts = toCountTable($n)

for d in '0'..'9':

dSwString.add $counts[d]

yield newInteger(dSwString.strip(leading = true, trailing = false, {'0'}))

echo "Known eight Smarandache-Wellin numbers which are prime:"

var idx, count = 0

for (n, p)in swNumbers():

inc idx

if n.isPrime:

inc count

echo &"{count}: index = {idx:<4} last prime = {p:<5} value = {compressed($n, 20)}"

if count == 8: break

echo "\nFirst 20 derived S-W numbers which are prime:"

idx = 0

count = 0

for n in derivedSwNumbers():

inc idx

if n.isPrime:

inc count

echo &"{count:2}: index = {idx:<4} value = {n}"

if count == 20: break

</syntaxhighlight>

{{out}}

<pre>Known eight Smarandache-Wellin numbers which are prime:

1: index = 1 last prime = 2 value = 2

2: index = 2 last prime = 3 value = 23

3: index = 4 last prime = 7 value = 2357

4: index = 128 last prime = 719 value = 23571113171923293137...73677683691701709719 (355 digits)

5: index = 174 last prime = 1033 value = 23571113171923293137...10131019102110311033 (499 digits)

6: index = 342 last prime = 2297 value = 23571113171923293137...22732281228722932297 (1171 digits)

7: index = 435 last prime = 3037 value = 23571113171923293137...30013011301930233037 (1543 digits)

8: index = 1429 last prime = 11927 value = 23571113171923293137...11903119091192311927 (5719 digits)

First 20 derived S-W numbers which are prime:

1: index = 32 value = 4194123321127

2: index = 72 value = 547233879626521

3: index = 73 value = 547233979727521

4: index = 134 value = 13672766322929571043

5: index = 225 value = 3916856106393739943689

6: index = 303 value = 462696313560586013558131

7: index = 309 value = 532727113760586013758133

8: index = 363 value = 6430314317473636515467149

9: index = 462 value = 8734722823685889120488197

10: index = 490 value = 9035923128899919621189209

11: index = 495 value = 9036023329699969621389211

12: index = 522 value = 9337023533410210710923191219

13: index = 538 value = 94374237357103109113243102223

14: index = 624 value = 117416265406198131121272110263

15: index = 721 value = 141459282456260193137317129313

16: index = 738 value = 144466284461264224139325131317

17: index = 790 value = 156483290479273277162351153339

18: index = 852 value = 164518312512286294233375158359

19: index = 1087 value = 208614364610327343341589284471

20: index = 1188 value = 229667386663354357356628334581

</pre>