Updated with fixes.

Author: Oren (electricessence)

README.md

@@ -3,3 +3,55 @@
 Methods and extensions for prime number detection and discovery.
 
 [![NuGet](https://img.shields.io/nuget/v/Open.Numeric.Primes.svg)](https://www.nuget.org/packages/Open.Numeric.Primes/)
+
+## Examples
+
+### Importing
+
+```cs
+using Open.Numeric.Primes;
+```
+
+### Primality Test
+
+```cs
+Number.IsPrime(8592868089022906369) // true
+```
+
+### Factors
+
+```cs
+Prime.Factors(12) // 2, 2, 3
+```
+
+### Common Factors
+
+```cs
+Prime.CommonFactors(84, 756, 108) // 2, 2, 3
+```
+
+### Greatest Factor
+
+```cs
+Prime.GreatestFactor(84, 756, 108) // 12
+```
+
+### Prime Discovery
+
+```cs
+// Will list the first 1000 primes.
+foreach(var prime in Prime.Numbers.Take(1000))
+{
+    Console.Write(prime);
+}
+```
+
+or
+
+```cs
+// Will list the first 1000 primes greater than (or equal to) 10,000.
+foreach(var prime in Prime.Numbers.StartingAt(10000).Take(100))
+{
+    Console.Write(prime);
+}
+```

source/Open.Numeric.Primes.csproj

@@ -11,12 +11,12 @@
 
 			Part of the "Open" set of libraries.
 		</Description>
-		<PackageTags>prime numbers;primes;prime factorization;prime detection;prime discovery</PackageTags>
+		<PackageTags>prime numbers;primes;prime factorization;prime detection;prime discovery;primality;primality test;factors;common factors;greatest factor;</PackageTags>
 		<Copyright>© electricessence (Oren F.) All rights reserved.</Copyright>
 		<PackageProjectUrl>https://github.com/Open-NET-Libraries/Open.Numeric.Primes/</PackageProjectUrl>
 		<RepositoryUrl>https://github.com/Open-NET-Libraries/Open.Numeric.Primes/</RepositoryUrl>
 		<RepositoryType>git</RepositoryType>
-		<Version>1.6.0</Version>
+		<Version>2.0.0</Version>
 		<PackageReleaseNotes></PackageReleaseNotes>
 		<PackageLicenseExpression>MIT</PackageLicenseExpression>
 		<PublishRepositoryUrl>true</PublishRepositoryUrl>

source/Polynomial.cs

@@ -4,11 +4,11 @@ namespace Open.Numeric.Primes
 {
 	public static class Polynomial
 	{
-		const ulong MAX_ULONG_DIVISOR = 4294967296UL;
+		const uint MAX_UINT_DIVISOR = 65536U;
 
-		internal static bool IsPrimeInternal(in ulong value)
+		internal static bool IsPrimeInternal(uint value)
 		{
-			ulong divisor = 6;
+			uint divisor = 6;
 			while (divisor * divisor - 2 * divisor + 1 <= value)
 			{
 				if (value % (divisor - 1) == 0)
@@ -19,17 +19,19 @@ internal static bool IsPrimeInternal(in ulong value)
 
 				divisor += 6;
 
-				if (divisor > MAX_ULONG_DIVISOR)
-					return IsPrime(value, divisor);
+				if (divisor > MAX_UINT_DIVISOR)
+					return IsPrimeInternal(value, divisor);
 			}
 			return true;
 		}
 
-		const uint MAX_UINT_DIVISOR = 65536U;
+		const ulong MAX_ULONG_DIVISOR = 4294967296UL;
 
-		internal static bool IsPrimeInternal(uint value)
+		internal static bool IsPrimeInternal(in ulong value, ulong divisor = 6)
 		{
-			uint divisor = 6;
+			if (divisor > MAX_ULONG_DIVISOR)
+				return IsPrime(value, divisor);
+
 			while (divisor * divisor - 2 * divisor + 1 <= value)
 			{
 				if (value % (divisor - 1) == 0)
@@ -40,9 +42,10 @@ internal static bool IsPrimeInternal(uint value)
 
 				divisor += 6;
 
-				if (divisor > MAX_UINT_DIVISOR)
+				if (divisor > MAX_ULONG_DIVISOR)
 					return IsPrime(value, divisor);
 			}
+
 			return true;
 		}
 

source/Primes.cs

@@ -479,6 +479,15 @@ public static long GreatestFactor(IEnumerable<long> values)
 		public static ulong GreatestFactor(IEnumerable<ulong> values)
 			=> CommonFactors(values).Aggregate(1UL, (p, c) => p * c);
 
+		/// <summary>
+		/// Returns the greatest common (positive) factor (GCF) of all the provided values.
+		/// Returns 1 if none found.
+		/// </summary>
+		/// <param name="values">The values to find common prime factors from.</param>
+		/// <returns>The greatest common factor or 1 if none found.</returns>
+		public static ulong GreatestFactor(params ulong[] values)
+			=> CommonFactors(values).Aggregate(1UL, (p, c) => p * c);
+
 		/// <summary>
 		/// Returns the greatest common (positive) factor (GCF) of all the provided values.
 		/// Returns 1 if none found.
@@ -487,6 +496,15 @@ public static ulong GreatestFactor(IEnumerable<ulong> values)
 		/// <returns>The greatest common factor or 1 if none found.</returns>
 		public static BigInteger GreatestFactor(IEnumerable<BigInteger> values)
 			=> CommonFactors(values).Aggregate(BigInteger.One, (p, c) => p * c);
+
+		/// <summary>
+		/// Returns the greatest common (positive) factor (GCF) of all the provided values.
+		/// Returns 1 if none found.
+		/// </summary>
+		/// <param name="values">The values to find common prime factors from.</param>
+		/// <returns>The greatest common factor or 1 if none found.</returns>
+		public static BigInteger GreatestFactor(params BigInteger[] values)
+			=> CommonFactors(values).Aggregate(BigInteger.One, (p, c) => p * c);
 	}