Cuban primes: Difference between revisions
Content added Content deleted
Thundergnat (talk | contribs) (Rename Perl 6 -> Raku, alphabetize, minor clean-up) |
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} |
} |
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</lang> |
</lang> |
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=={{header|C sharp|C#}}== |
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{{trans|Visual Basic .NET}} |
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(of the Snail Version) |
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<lang csharp>using System; |
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using System.Collections.Generic; |
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using System.Linq; |
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static class Program |
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{ |
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static List<long> primes = new List<long>() { 3, 5 }; |
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static void Main(string[] args) |
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{ |
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const int cutOff = 200; |
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const int bigUn = 100000; |
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const int chunks = 50; |
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const int little = bigUn / chunks; |
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const string tn = " cuban prime"; |
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Console.WriteLine("The first {0:n0}{1}s:", cutOff, tn); |
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int c = 0; |
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bool showEach = true; |
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long u = 0, v = 1; |
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DateTime st = DateTime.Now; |
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for (long i = 1; i <= long.MaxValue; i++) |
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{ |
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bool found = false; |
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int mx = System.Convert.ToInt32(Math.Ceiling(Math.Sqrt(v += (u += 6)))); |
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foreach (long item in primes) |
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{ |
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if (item > mx) break; |
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if (v % item == 0) { found = true; break; } |
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} |
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if (!found) |
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{ |
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c += 1; if (showEach) |
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{ |
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for (var z = primes.Last() + 2; z <= v - 2; z += 2) |
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{ |
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bool fnd = false; |
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foreach (long item in primes) |
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{ |
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if (item > mx) break; |
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if (z % item == 0) { fnd = true; break; } |
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} |
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if (!fnd) primes.Add(z); |
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} |
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primes.Add(v); Console.Write("{0,11:n0}", v); |
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if (c % 10 == 0) Console.WriteLine(); |
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if (c == cutOff) |
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{ |
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showEach = false; |
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Console.Write("\nProgress to the {0:n0}th{1}: ", bigUn, tn); |
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} |
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} |
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if (c % little == 0) { Console.Write("."); if (c == bigUn) break; } |
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} |
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} |
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Console.WriteLine("\nThe {1:n0}th{2} is {0,17:n0}", v, c, tn); |
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Console.WriteLine("Computation time was {0} seconds", (DateTime.Now - st).TotalSeconds); |
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if (System.Diagnostics.Debugger.IsAttached) Console.ReadKey(); |
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} |
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}</lang> |
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{{out}} |
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<pre>The first 200 cuban primes: |
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7 19 37 61 127 271 331 397 547 631 |
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919 1,657 1,801 1,951 2,269 2,437 2,791 3,169 3,571 4,219 |
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4,447 5,167 5,419 6,211 7,057 7,351 8,269 9,241 10,267 11,719 |
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12,097 13,267 13,669 16,651 19,441 19,927 22,447 23,497 24,571 25,117 |
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26,227 27,361 33,391 35,317 42,841 45,757 47,251 49,537 50,311 55,897 |
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59,221 60,919 65,269 70,687 73,477 74,419 75,367 81,181 82,171 87,211 |
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88,237 89,269 92,401 96,661 102,121 103,231 104,347 110,017 112,327 114,661 |
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115,837 126,691 129,169 131,671 135,469 140,617 144,541 145,861 151,201 155,269 |
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163,567 169,219 170,647 176,419 180,811 189,757 200,467 202,021 213,067 231,019 |
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234,361 241,117 246,247 251,431 260,191 263,737 267,307 276,337 279,991 283,669 |
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285,517 292,969 296,731 298,621 310,087 329,677 333,667 337,681 347,821 351,919 |
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360,187 368,551 372,769 374,887 377,011 383,419 387,721 398,581 407,377 423,001 |
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436,627 452,797 459,817 476,407 478,801 493,291 522,919 527,941 553,411 574,219 |
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584,767 590,077 592,741 595,411 603,457 608,851 611,557 619,711 627,919 650,071 |
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658,477 666,937 689,761 692,641 698,419 707,131 733,591 742,519 760,537 769,627 |
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772,669 784,897 791,047 812,761 825,301 837,937 847,477 863,497 879,667 886,177 |
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895,987 909,151 915,769 925,741 929,077 932,419 939,121 952,597 972,991 976,411 |
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986,707 990,151 997,057 1,021,417 1,024,921 1,035,469 1,074,607 1,085,407 1,110,817 1,114,471 |
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1,125,469 1,155,061 1,177,507 1,181,269 1,215,397 1,253,887 1,281,187 1,285,111 1,324,681 1,328,671 |
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1,372,957 1,409,731 1,422,097 1,426,231 1,442,827 1,451,161 1,480,519 1,484,737 1,527,247 1,570,357 |
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Progress to the 100,000th cuban prime: .................................................. |
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The 100,000th cuban prime is 1,792,617,147,127 |
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Computation time was 63.578673 seconds</pre> |
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=={{header|C++}}== |
=={{header|C++}}== |
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Line 502: | Line 591: | ||
The 100,000th cuban prime is 1,792,617,147,127 |
The 100,000th cuban prime is 1,792,617,147,127 |
||
Computation time was 35.5644 seconds</pre> |
Computation time was 35.5644 seconds</pre> |
||
=={{header|C#}}== |
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{{trans|Visual Basic .NET}} |
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(of the Snail Version) |
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<lang csharp>using System; |
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using System.Collections.Generic; |
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using System.Linq; |
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static class Program |
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{ |
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static List<long> primes = new List<long>() { 3, 5 }; |
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static void Main(string[] args) |
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{ |
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const int cutOff = 200; |
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const int bigUn = 100000; |
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const int chunks = 50; |
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const int little = bigUn / chunks; |
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const string tn = " cuban prime"; |
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Console.WriteLine("The first {0:n0}{1}s:", cutOff, tn); |
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int c = 0; |
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bool showEach = true; |
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long u = 0, v = 1; |
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DateTime st = DateTime.Now; |
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for (long i = 1; i <= long.MaxValue; i++) |
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{ |
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bool found = false; |
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int mx = System.Convert.ToInt32(Math.Ceiling(Math.Sqrt(v += (u += 6)))); |
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foreach (long item in primes) |
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{ |
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if (item > mx) break; |
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if (v % item == 0) { found = true; break; } |
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} |
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if (!found) |
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{ |
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c += 1; if (showEach) |
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{ |
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for (var z = primes.Last() + 2; z <= v - 2; z += 2) |
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{ |
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bool fnd = false; |
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foreach (long item in primes) |
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{ |
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if (item > mx) break; |
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if (z % item == 0) { fnd = true; break; } |
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} |
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if (!fnd) primes.Add(z); |
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} |
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primes.Add(v); Console.Write("{0,11:n0}", v); |
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if (c % 10 == 0) Console.WriteLine(); |
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if (c == cutOff) |
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{ |
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showEach = false; |
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Console.Write("\nProgress to the {0:n0}th{1}: ", bigUn, tn); |
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} |
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} |
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if (c % little == 0) { Console.Write("."); if (c == bigUn) break; } |
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} |
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} |
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Console.WriteLine("\nThe {1:n0}th{2} is {0,17:n0}", v, c, tn); |
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Console.WriteLine("Computation time was {0} seconds", (DateTime.Now - st).TotalSeconds); |
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if (System.Diagnostics.Debugger.IsAttached) Console.ReadKey(); |
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} |
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}</lang> |
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{{out}} |
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<pre>The first 200 cuban primes: |
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7 19 37 61 127 271 331 397 547 631 |
|||
919 1,657 1,801 1,951 2,269 2,437 2,791 3,169 3,571 4,219 |
|||
4,447 5,167 5,419 6,211 7,057 7,351 8,269 9,241 10,267 11,719 |
|||
12,097 13,267 13,669 16,651 19,441 19,927 22,447 23,497 24,571 25,117 |
|||
26,227 27,361 33,391 35,317 42,841 45,757 47,251 49,537 50,311 55,897 |
|||
59,221 60,919 65,269 70,687 73,477 74,419 75,367 81,181 82,171 87,211 |
|||
88,237 89,269 92,401 96,661 102,121 103,231 104,347 110,017 112,327 114,661 |
|||
115,837 126,691 129,169 131,671 135,469 140,617 144,541 145,861 151,201 155,269 |
|||
163,567 169,219 170,647 176,419 180,811 189,757 200,467 202,021 213,067 231,019 |
|||
234,361 241,117 246,247 251,431 260,191 263,737 267,307 276,337 279,991 283,669 |
|||
285,517 292,969 296,731 298,621 310,087 329,677 333,667 337,681 347,821 351,919 |
|||
360,187 368,551 372,769 374,887 377,011 383,419 387,721 398,581 407,377 423,001 |
|||
436,627 452,797 459,817 476,407 478,801 493,291 522,919 527,941 553,411 574,219 |
|||
584,767 590,077 592,741 595,411 603,457 608,851 611,557 619,711 627,919 650,071 |
|||
658,477 666,937 689,761 692,641 698,419 707,131 733,591 742,519 760,537 769,627 |
|||
772,669 784,897 791,047 812,761 825,301 837,937 847,477 863,497 879,667 886,177 |
|||
895,987 909,151 915,769 925,741 929,077 932,419 939,121 952,597 972,991 976,411 |
|||
986,707 990,151 997,057 1,021,417 1,024,921 1,035,469 1,074,607 1,085,407 1,110,817 1,114,471 |
|||
1,125,469 1,155,061 1,177,507 1,181,269 1,215,397 1,253,887 1,281,187 1,285,111 1,324,681 1,328,671 |
|||
1,372,957 1,409,731 1,422,097 1,426,231 1,442,827 1,451,161 1,480,519 1,484,737 1,527,247 1,570,357 |
|||
Progress to the 100,000th cuban prime: .................................................. |
|||
The 100,000th cuban prime is 1,792,617,147,127 |
|||
Computation time was 63.578673 seconds</pre> |
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=={{header|D}}== |
=={{header|D}}== |
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Line 845: | Line 845: | ||
The 100,000th cuban prime is 1,792,617,147,127 |
The 100,000th cuban prime is 1,792,617,147,127 |
||
</pre> |
</pre> |
||
=={{header|J}}== |
=={{header|J}}== |
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Line 1,586: | Line 1,585: | ||
10^6-th cuban prime is: 255,155,578,239,277 |
10^6-th cuban prime is: 255,155,578,239,277 |
||
</pre> |
</pre> |
||
=={{header|Perl 6}}== |
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{{works with|Rakudo|2018.12}} |
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===The task (k == 1)=== |
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Not the most efficient, but concise, and good enough for this task. Use the ntheory library for prime testing; gets it down to around 20 seconds. |
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<lang perl6>use Lingua::EN::Numbers; |
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use ntheory:from<Perl5> <:all>; |
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my @cubans = lazy (1..Inf).map({ ($_+1)³ - .³ }).grep: *.&is_prime; |
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put @cubans[^200]».&comma».fmt("%9s").rotor(10).join: "\n"; |
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put ''; |
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put @cubans[99_999]., # zero indexed</lang> |
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{{out}} |
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<pre> 7 19 37 61 127 271 331 397 547 631 |
|||
919 1,657 1,801 1,951 2,269 2,437 2,791 3,169 3,571 4,219 |
|||
4,447 5,167 5,419 6,211 7,057 7,351 8,269 9,241 10,267 11,719 |
|||
12,097 13,267 13,669 16,651 19,441 19,927 22,447 23,497 24,571 25,117 |
|||
26,227 27,361 33,391 35,317 42,841 45,757 47,251 49,537 50,311 55,897 |
|||
59,221 60,919 65,269 70,687 73,477 74,419 75,367 81,181 82,171 87,211 |
|||
88,237 89,269 92,401 96,661 102,121 103,231 104,347 110,017 112,327 114,661 |
|||
115,837 126,691 129,169 131,671 135,469 140,617 144,541 145,861 151,201 155,269 |
|||
163,567 169,219 170,647 176,419 180,811 189,757 200,467 202,021 213,067 231,019 |
|||
234,361 241,117 246,247 251,431 260,191 263,737 267,307 276,337 279,991 283,669 |
|||
285,517 292,969 296,731 298,621 310,087 329,677 333,667 337,681 347,821 351,919 |
|||
360,187 368,551 372,769 374,887 377,011 383,419 387,721 398,581 407,377 423,001 |
|||
436,627 452,797 459,817 476,407 478,801 493,291 522,919 527,941 553,411 574,219 |
|||
584,767 590,077 592,741 595,411 603,457 608,851 611,557 619,711 627,919 650,071 |
|||
658,477 666,937 689,761 692,641 698,419 707,131 733,591 742,519 760,537 769,627 |
|||
772,669 784,897 791,047 812,761 825,301 837,937 847,477 863,497 879,667 886,177 |
|||
895,987 909,151 915,769 925,741 929,077 932,419 939,121 952,597 972,991 976,411 |
|||
986,707 990,151 997,057 1,021,417 1,024,921 1,035,469 1,074,607 1,085,407 1,110,817 1,114,471 |
|||
1,125,469 1,155,061 1,177,507 1,181,269 1,215,397 1,253,887 1,281,187 1,285,111 1,324,681 1,328,671 |
|||
1,372,957 1,409,731 1,422,097 1,426,231 1,442,827 1,451,161 1,480,519 1,484,737 1,527,247 1,570,357 |
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1,792,617,147,127</pre> |
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===k == 2 through 10=== |
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After reading up a bit, the general equation for cuban primes is prime numbers of the form {{math|((<var>x</var>+<var>k</var>)<sup>3</sup> - <var>x</var><sup>3</sup>)/<var>k</var> }} where k mod 3 is not equal 0. |
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The cubans where k == 1 (the focus of this task) is one of many possible groups. In general, it seems like the cubans where k == 1 and k == 2 are the two primary cases, but it is possible to have cubans with a k of any integer that is not a multiple of 3. |
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Here are the first 20 for each valid k up to 10: |
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<lang perl6>sub comma { $^i.flip.comb(3).join(',').flip } |
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for 2..10 -> \k { |
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next if k %% 3; |
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my @cubans = lazy (1..Inf).map({ (($_+k)³ - .³)/k }).grep: *.is-prime; |
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put "First 20 cuban primes where k = {k}:"; |
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put @cubans[^20]».&comma».fmt("%7s").rotor(10).join: "\n"; |
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put ''; |
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} |
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</lang> |
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{{out}} |
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<pre>First 20 cuban primes where k = 2: |
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13 109 193 433 769 1,201 1,453 2,029 3,469 3,889 |
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4,801 10,093 12,289 13,873 18,253 20,173 21,169 22,189 28,813 37,633 |
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First 20 cuban primes where k = 4: |
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31 79 151 367 1,087 1,327 1,879 2,887 3,271 4,111 |
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4,567 6,079 7,207 8,431 15,991 16,879 17,791 19,687 23,767 24,847 |
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First 20 cuban primes where k = 5: |
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43 67 97 223 277 337 727 823 1,033 1,663 |
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2,113 2,617 2,797 3,373 4,003 5,683 6,217 7,963 10,273 10,627 |
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First 20 cuban primes where k = 7: |
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73 103 139 181 229 283 409 643 733 829 |
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1,039 1,153 1,399 1,531 1,669 2,281 2,803 3,181 3,583 3,793 |
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First 20 cuban primes where k = 8: |
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163 379 523 691 883 2,203 2,539 3,691 5,059 5,563 |
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6,091 7,219 8,443 9,091 10,459 11,923 15,139 19,699 24,859 27,091 |
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First 20 cuban primes where k = 10: |
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457 613 997 1,753 2,053 2,377 4,357 6,373 9,433 13,093 |
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16,453 21,193 27,673 28,837 31,237 37,657 46,153 47,653 49,177 62,233</pre> |
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===k == 2^128=== |
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Note that Perl 6 has native support for arbitrarily large integers and does not need to generate primes to test for primality. Using k of 2^128; finishes in ''well'' under a second. |
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<lang perl6>sub comma { $^i.flip.comb(3).join(',').flip } |
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my \k = 2**128; |
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put "First 10 cuban primes where k = {k}:"; |
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.&comma.put for (lazy (0..Inf).map({ (($_+k)³ - .³)/k }).grep: *.is-prime)[^10];</lang> |
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<pre>First 10 cuban primes where k = 340282366920938463463374607431768211456: |
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115,792,089,237,316,195,423,570,985,008,687,908,160,544,961,995,247,996,546,884,854,518,799,824,856,507 |
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115,792,089,237,316,195,423,570,985,008,687,908,174,836,821,405,927,412,012,346,588,030,934,089,763,531 |
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115,792,089,237,316,195,423,570,985,008,687,908,219,754,093,839,491,289,189,512,036,211,927,493,764,691 |
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115,792,089,237,316,195,423,570,985,008,687,908,383,089,629,961,541,751,651,931,847,779,176,235,685,011 |
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115,792,089,237,316,195,423,570,985,008,687,908,491,299,422,642,400,183,033,284,972,942,478,527,291,811 |
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115,792,089,237,316,195,423,570,985,008,687,908,771,011,528,251,411,600,000,178,900,251,391,998,361,371 |
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115,792,089,237,316,195,423,570,985,008,687,908,875,137,932,529,218,769,819,971,530,125,513,071,648,307 |
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115,792,089,237,316,195,423,570,985,008,687,908,956,805,700,590,244,001,051,181,435,909,137,442,897,427 |
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115,792,089,237,316,195,423,570,985,008,687,909,028,264,997,643,641,078,378,490,103,469,808,767,771,907 |
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115,792,089,237,316,195,423,570,985,008,687,909,158,933,426,541,281,448,348,425,952,723,607,761,904,131</pre> |
|||
=={{header|Phix}}== |
=={{header|Phix}}== |
||
Line 1,911: | Line 1,810: | ||
|.........|.........|.........|.........|.........|.........|.........|.........|.........|......... |
|.........|.........|.........|.........|.........|.........|.........|.........|.........|......... |
||
1792617147127</pre> |
1792617147127</pre> |
||
=={{header|Raku}}== |
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(formerly Perl 6) |
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{{works with|Rakudo|2018.12}} |
|||
===The task (k == 1)=== |
|||
Not the most efficient, but concise, and good enough for this task. Use the ntheory library for prime testing; gets it down to around 20 seconds. |
|||
<lang perl6>use Lingua::EN::Numbers; |
|||
use ntheory:from<Perl5> <:all>; |
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my @cubans = lazy (1..Inf).map({ ($_+1)³ - .³ }).grep: *.&is_prime; |
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put @cubans[^200]».&comma».fmt("%9s").rotor(10).join: "\n"; |
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put ''; |
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put @cubans[99_999]., # zero indexed</lang> |
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{{out}} |
|||
<pre> 7 19 37 61 127 271 331 397 547 631 |
|||
919 1,657 1,801 1,951 2,269 2,437 2,791 3,169 3,571 4,219 |
|||
4,447 5,167 5,419 6,211 7,057 7,351 8,269 9,241 10,267 11,719 |
|||
12,097 13,267 13,669 16,651 19,441 19,927 22,447 23,497 24,571 25,117 |
|||
26,227 27,361 33,391 35,317 42,841 45,757 47,251 49,537 50,311 55,897 |
|||
59,221 60,919 65,269 70,687 73,477 74,419 75,367 81,181 82,171 87,211 |
|||
88,237 89,269 92,401 96,661 102,121 103,231 104,347 110,017 112,327 114,661 |
|||
115,837 126,691 129,169 131,671 135,469 140,617 144,541 145,861 151,201 155,269 |
|||
163,567 169,219 170,647 176,419 180,811 189,757 200,467 202,021 213,067 231,019 |
|||
234,361 241,117 246,247 251,431 260,191 263,737 267,307 276,337 279,991 283,669 |
|||
285,517 292,969 296,731 298,621 310,087 329,677 333,667 337,681 347,821 351,919 |
|||
360,187 368,551 372,769 374,887 377,011 383,419 387,721 398,581 407,377 423,001 |
|||
436,627 452,797 459,817 476,407 478,801 493,291 522,919 527,941 553,411 574,219 |
|||
584,767 590,077 592,741 595,411 603,457 608,851 611,557 619,711 627,919 650,071 |
|||
658,477 666,937 689,761 692,641 698,419 707,131 733,591 742,519 760,537 769,627 |
|||
772,669 784,897 791,047 812,761 825,301 837,937 847,477 863,497 879,667 886,177 |
|||
895,987 909,151 915,769 925,741 929,077 932,419 939,121 952,597 972,991 976,411 |
|||
986,707 990,151 997,057 1,021,417 1,024,921 1,035,469 1,074,607 1,085,407 1,110,817 1,114,471 |
|||
1,125,469 1,155,061 1,177,507 1,181,269 1,215,397 1,253,887 1,281,187 1,285,111 1,324,681 1,328,671 |
|||
1,372,957 1,409,731 1,422,097 1,426,231 1,442,827 1,451,161 1,480,519 1,484,737 1,527,247 1,570,357 |
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1,792,617,147,127</pre> |
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===k == 2 through 10=== |
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After reading up a bit, the general equation for cuban primes is prime numbers of the form {{math|((<var>x</var>+<var>k</var>)<sup>3</sup> - <var>x</var><sup>3</sup>)/<var>k</var> }} where k mod 3 is not equal 0. |
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The cubans where k == 1 (the focus of this task) is one of many possible groups. In general, it seems like the cubans where k == 1 and k == 2 are the two primary cases, but it is possible to have cubans with a k of any integer that is not a multiple of 3. |
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Here are the first 20 for each valid k up to 10: |
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<lang perl6>sub comma { $^i.flip.comb(3).join(',').flip } |
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for 2..10 -> \k { |
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next if k %% 3; |
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my @cubans = lazy (1..Inf).map({ (($_+k)³ - .³)/k }).grep: *.is-prime; |
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put "First 20 cuban primes where k = {k}:"; |
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put @cubans[^20]».&comma».fmt("%7s").rotor(10).join: "\n"; |
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put ''; |
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} |
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</lang> |
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{{out}} |
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<pre>First 20 cuban primes where k = 2: |
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13 109 193 433 769 1,201 1,453 2,029 3,469 3,889 |
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4,801 10,093 12,289 13,873 18,253 20,173 21,169 22,189 28,813 37,633 |
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First 20 cuban primes where k = 4: |
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31 79 151 367 1,087 1,327 1,879 2,887 3,271 4,111 |
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4,567 6,079 7,207 8,431 15,991 16,879 17,791 19,687 23,767 24,847 |
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First 20 cuban primes where k = 5: |
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43 67 97 223 277 337 727 823 1,033 1,663 |
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2,113 2,617 2,797 3,373 4,003 5,683 6,217 7,963 10,273 10,627 |
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First 20 cuban primes where k = 7: |
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73 103 139 181 229 283 409 643 733 829 |
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1,039 1,153 1,399 1,531 1,669 2,281 2,803 3,181 3,583 3,793 |
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First 20 cuban primes where k = 8: |
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163 379 523 691 883 2,203 2,539 3,691 5,059 5,563 |
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6,091 7,219 8,443 9,091 10,459 11,923 15,139 19,699 24,859 27,091 |
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First 20 cuban primes where k = 10: |
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457 613 997 1,753 2,053 2,377 4,357 6,373 9,433 13,093 |
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16,453 21,193 27,673 28,837 31,237 37,657 46,153 47,653 49,177 62,233</pre> |
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===k == 2^128=== |
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Note that Perl 6 has native support for arbitrarily large integers and does not need to generate primes to test for primality. Using k of 2^128; finishes in ''well'' under a second. |
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<lang perl6>sub comma { $^i.flip.comb(3).join(',').flip } |
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my \k = 2**128; |
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put "First 10 cuban primes where k = {k}:"; |
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.&comma.put for (lazy (0..Inf).map({ (($_+k)³ - .³)/k }).grep: *.is-prime)[^10];</lang> |
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<pre>First 10 cuban primes where k = 340282366920938463463374607431768211456: |
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115,792,089,237,316,195,423,570,985,008,687,908,160,544,961,995,247,996,546,884,854,518,799,824,856,507 |
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115,792,089,237,316,195,423,570,985,008,687,908,174,836,821,405,927,412,012,346,588,030,934,089,763,531 |
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115,792,089,237,316,195,423,570,985,008,687,908,219,754,093,839,491,289,189,512,036,211,927,493,764,691 |
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115,792,089,237,316,195,423,570,985,008,687,908,383,089,629,961,541,751,651,931,847,779,176,235,685,011 |
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115,792,089,237,316,195,423,570,985,008,687,908,491,299,422,642,400,183,033,284,972,942,478,527,291,811 |
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115,792,089,237,316,195,423,570,985,008,687,908,771,011,528,251,411,600,000,178,900,251,391,998,361,371 |
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115,792,089,237,316,195,423,570,985,008,687,908,875,137,932,529,218,769,819,971,530,125,513,071,648,307 |
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115,792,089,237,316,195,423,570,985,008,687,908,956,805,700,590,244,001,051,181,435,909,137,442,897,427 |
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115,792,089,237,316,195,423,570,985,008,687,909,028,264,997,643,641,078,378,490,103,469,808,767,771,907 |
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115,792,089,237,316,195,423,570,985,008,687,909,158,933,426,541,281,448,348,425,952,723,607,761,904,131</pre> |
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=={{header|REXX}}== |
=={{header|REXX}}== |