Factorial primes: Difference between revisions
Nim solution.
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(Nim solution.) |
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9: 12! - 1 = 479001599
10: 14! - 1 = 87178291199
</pre>
=={{header|Nim}}==
{{libheader|integers}}
Nim standard integer types are limited to 64 bits. So we use an external library which provides arbitrary sized integers.
<syntaxhighlight lang="nim">import std/[math, strformat]
# Task.
func isPrime(n: int): bool =
if n < 2: return false
if n == 2 or n == 3: return true
if n mod 2 == 0: return false
if n mod 3 == 0: return false
var d = 5
var step = 2
while d * d <= n:
if n mod d == 0:
return false
inc d, step
step = 6 - step
return true
echo "First 10 factorial primes:\n"
var count = 0
var n = 1
while count < 10:
let f = fac(n)
if isPrime(f - 1):
inc count
echo &"{count:>2}: {n:>3}! - 1 = {f - 1}"
if count < 10 and isPrime(f + 1):
inc count
echo &"{count:>2}: {n:>3}! + 1 = {f + 1}"
inc n
# Stretch.
import integers
func str(n: Integer): string =
## Return the string representation of an Integer.
result = $n
if result.len > 40:
result = &"{result[0..19]}...{result[^20..^1]} ({result.len} digits)"
echo "\n\nNext 20 factorial primes:\n"
while count < 30:
let f: Integer = factorial(n)
if isPrime(f - 1):
inc count
echo &"{count:>2}: {n:>3}! - 1 = {str(f - 1)}"
if isPrime(f + 1):
inc count
echo &"{count:>2}: {n:>3}! - 1 = {str(f + 1)}"
inc n
</syntaxhighlight>
{{out}}
<pre>First 10 factorial primes:
1: 1! + 1 = 2
2: 2! + 1 = 3
3: 3! - 1 = 5
4: 3! + 1 = 7
5: 4! - 1 = 23
6: 6! - 1 = 719
7: 7! - 1 = 5039
8: 11! + 1 = 39916801
9: 12! - 1 = 479001599
10: 14! - 1 = 87178291199
Next 20 factorial primes:
11: 27! - 1 = 10888869450418352160768000001
12: 30! - 1 = 265252859812191058636308479999999
13: 32! - 1 = 263130836933693530167218012159999999
14: 33! - 1 = 8683317618811886495518194401279999999
15: 37! - 1 = 13763753091226345046...79581580902400000001 (44 digits)
16: 38! - 1 = 52302261746660111176...24100074291199999999 (45 digits)
17: 41! - 1 = 33452526613163807108...40751665152000000001 (50 digits)
18: 73! - 1 = 44701154615126843408...03680000000000000001 (106 digits)
19: 77! - 1 = 14518309202828586963...48000000000000000001 (114 digits)
20: 94! - 1 = 10873661566567430802...99999999999999999999 (147 digits)
21: 116! - 1 = 33931086844518982011...00000000000000000001 (191 digits)
22: 154! - 1 = 30897696138473508879...00000000000000000001 (272 digits)
23: 166! - 1 = 90036917057784373664...99999999999999999999 (298 digits)
24: 320! - 1 = 21161033472192524829...00000000000000000001 (665 digits)
25: 324! - 1 = 22889974601791023211...99999999999999999999 (675 digits)
26: 340! - 1 = 51008644721037110809...00000000000000000001 (715 digits)
27: 379! - 1 = 24840307460964707050...99999999999999999999 (815 digits)
28: 399! - 1 = 16008630711655973815...00000000000000000001 (867 digits)
29: 427! - 1 = 29063471769607348411...00000000000000000001 (940 digits)
30: 469! - 1 = 67718096668149510900...99999999999999999999 (1051 digits)
</pre>
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