Twin primes: Difference between revisions
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Number of twin prime pairs less than 100,000,000,000 is 224,376,048
</pre>
=={{header|C sharp}}==
Runs in about 18 seconds.
<lang csharp>using System;
using System.Linq;
using System.Collections;
using System.Collections.Generic;
public static class TwinPrimes
{
public static void Main()
{
CountTwinPrimes(Enumerable.Range(1, 9).Select(i => (int)Math.Pow(10, i)).ToArray());
}
private static void CountTwinPrimes(params int[] bounds)
{
Array.Sort(bounds);
int b = 0;
int count = 0;
string format = "There are {0:N0} twin primes below {1:N0}";
foreach (var twin in FindTwinPrimes(bounds[^1])) {
if (twin.p2 >= bounds[b]) {
Console.WriteLine(format, count, bounds[b]);
b++;
}
count++;
}
Console.WriteLine(format, count, bounds[b]);
}
private static IEnumerable<(int p1, int p2)> FindTwinPrimes(int bound) =>
PrimeSieve(bound).Pairwise().Where(pair => pair.p1 + 2 == pair.p2);
private static IEnumerable<int> PrimeSieve(int bound)
{
if (bound < 2) yield break;
yield return 2;
var composite = new BitArray((bound - 1) / 2);
int limit = (int)(Math.Sqrt(bound) - 1) / 2;
for (int i = 0; i < limit; i++) {
if (composite[i]) continue;
int prime = 2 * i + 3;
yield return prime;
for (int j = (prime * prime - 2) / 2; j < composite.Count; j += prime) {
composite[j] = true;
}
}
for (int i = limit; i < composite.Count; i++) {
if (!composite[i]) yield return 2 * i + 3;
}
}
private static IEnumerable<(T p1, T p2)> Pairwise<T>(this IEnumerable<T> source)
{
using var e = numbers.GetEnumerator();
if (!e.MoveNext()) yield break;
T p1 = e.Current;
while (e.MoveNext()) {
T p2 = e.Current;
yield return (p1, p2);
p1 = p2;
}
}
}</lang>
{{out}}
<pre style="height:30ex;overflow:scroll">
There are 2 twin primes below 10
There are 8 twin primes below 100
There are 35 twin primes below 1,000
There are 205 twin primes below 10,000
There are 1,224 twin primes below 100,000
There are 8,169 twin primes below 1,000,000
There are 58,980 twin primes below 10,000,000
There are 440,312 twin primes below 100,000,000
There are 3,424,506 twin primes below 1,000,000,000</pre>
=={{header|Delphi}}==
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