Fortunate numbers: Difference between revisions

</pre>

=={{header|C#}}==

{{trans|Java}}

<syntaxhighlight lang="C#">

using System;

using System.Collections.Generic;

using System.Numerics;

public class FortunateNumbers

{

private const int CERTAINTY_LEVEL = 10;

public static void Main(string[] args)

{

var primes = PrimeSieve(400);

SortedSet<int> fortunates = new SortedSet<int>();

BigInteger primorial = BigInteger.One;

foreach (var prime in primes)

{

primorial *= prime;

int candidate = 3;

while (!BigInteger.Add(primorial, candidate).IsProbablyPrime(CERTAINTY_LEVEL))

{

candidate += 2;

}

fortunates.Add(candidate);

}

Console.WriteLine("The first 50 distinct fortunate numbers are:");

int count = 0;

foreach (var fortunate in fortunates)

{

if (count >= 50) break;

Console.Write($"{fortunate,4}{(count % 10 == 9 ? "\n" : "")}");

count++;

}

}

private static List<int> PrimeSieve(int aNumber)

{

var sieve = new bool[aNumber + 1];

var primes = new List<int>();

for (int i = 2; i <= aNumber; i++)

{

if (!sieve[i])

{

primes.Add(i);

for (int j = i * i; j <= aNumber && j > 0; j += i)

{

sieve[j] = true;

}

}

}

return primes;

}

}

public static class BigIntegerExtensions

{

private static Random random = new Random();

public static bool IsProbablyPrime(this BigInteger source, int certainty)

{

if (source == 2 || source == 3)

return true;

if (source < 2 || source % 2 == 0)

return false;

BigInteger d = source - 1;

int s = 0;

while (d % 2 == 0)

{

d /= 2;

s += 1;

}

for (int i = 0; i < certainty; i++)

{

BigInteger a = RandomBigInteger(2, source - 2);

BigInteger x = BigInteger.ModPow(a, d, source);

if (x == 1 || x == source - 1)

continue;

for (int r = 1; r < s; r++)

{

x = BigInteger.ModPow(x, 2, source);

if (x == 1)

return false;

if (x == source - 1)

break;

}

if (x != source - 1)

return false;

}

return true;

}

private static BigInteger RandomBigInteger(BigInteger minValue, BigInteger maxValue)

{

if (minValue > maxValue)

throw new ArgumentException("minValue must be less than or equal to maxValue");

BigInteger range = maxValue - minValue + 1;

int length = range.ToByteArray().Length;

byte[] buffer = new byte[length];

BigInteger result;

do

{

random.NextBytes(buffer);

buffer[buffer.Length - 1] &= 0x7F; // Ensure non-negative

result = new BigInteger(buffer);

} while (result < minValue || result >= maxValue);

return result;

}

}

</syntaxhighlight>

{{out}}

<pre>

The first 50 distinct fortunate numbers are:

3 5 7 13 17 19 23 37 47 59

61 67 71 79 89 101 103 107 109 127

151 157 163 167 191 197 199 223 229 233

239 271 277 283 293 307 311 313 331 353

373 379 383 397 401 409 419 421 439 443