Prime Numbers in C# QuickStart Sample

Illustrates working with prime numbers and the IntegerMath class in the Numerics.NET namespace in C#.

This sample is also available in: Visual Basic, F#, IronPython.

Overview

This QuickStart sample demonstrates how to work with prime numbers using the IntegerMath class from Numerics.NET. The sample shows essential operations for working with prime numbers and factorization.

The sample illustrates several key capabilities:

• Factoring integers into their prime components, including handling of repeated factors
• Testing numbers for primality using the IsPrime method
• Finding the next prime number greater than a given value
• Finding the previous prime number less than a given value
• Working with large numbers up to 48 bits in length

The code demonstrates practical applications like:

• Decomposing composite numbers into their prime factors with multiplicity
• Verifying whether large numbers are prime
• Generating sequences of consecutive prime numbers both forward and backward
• Handling edge cases with large integers and repeated factors

All operations use efficient algorithms optimized for performance while maintaining numerical accuracy.

The code

using System;
// We use many classes from the Numerics.NET.SpecialFunctions
// namespace.
using Numerics.NET;

// Illustrates working with prime numbers using the
// IntegerMath class in the Numerics.NET.SpecialFunctions
// namespace of Numerics.NET.

// The license is verified at runtime. We're using
// a 30 day trial key here. For more information, see
//     https://numerics.net/trial-key
Numerics.NET.License.Verify("your-trial-key-here");

//
// Factoring numbers
//

// The Factor method returns a sequence of pairs of the prime factors
// and their multiplicity:
int index;

int n = 1001110110;
var factors = IntegerMath.Factor(n);
Console.Write($"{n} = ");
foreach (var factor in factors)
{
    Console.Write($" * {factor.Item1}");
    if (factor.Item2 > 1)
        Console.Write($"^{factor.Item2}");
}
Console.WriteLine();

// Factors that occur multiple times is repeated as many times as necessary:
n = 256 * 6157413;
factors = IntegerMath.Factor(n);
Console.Write($"{n} = ");
foreach (var factor in factors)
{
    Console.Write($" * {factor.Item1}");
    if (factor.Item2 > 1)
        Console.Write($"^{factor.Item2}");
}
Console.WriteLine();

// The 64bit version can safely factor numbers up to 48 bits long:
long n2 = 1296523 * 1177157L;
Console.Write($"{n2} = ");
foreach (var factor in factors)
{
    Console.Write($" * {factor.Item1}");
    if (factor.Item2 > 1)
        Console.Write($"^{factor.Item2}");
}
Console.WriteLine();

//
// Prime numbers
//

// The IsPrime method verifies if a number is prime or not.
n = 801853937;
Console.WriteLine("{0} is prime? {1}!", n, IntegerMath.IsPrime(n));
n = 801853939;
Console.WriteLine("{0} is prime? {1}!", n, IntegerMath.IsPrime(n));

// MextPrime gets the first prime after a specified number.
// You can call it repeatedly to get successive primes.
// Let//s get the 10 smallest primes larger than one billion:
n = 1000000000;
Console.WriteLine("\nFirst 10 primes greater than 1 billion:");
for(index = 0; index < 10; index++)
{
    n = IntegerMath.NextPrime(n);
    Console.Write("{0,16}", n);
}
Console.WriteLine();

// PreviousPrime gets the last prime before a specified number.
n = 1000000000;
Console.WriteLine("Last 10 primes less than 1 billion:");
for(index = 0; index < 10; index++)
{
    n = IntegerMath.PreviousPrime(n);
    Console.Write("{0,16}", n);
}
Console.WriteLine();

Console.Write("Press Enter key to exit...");
Console.ReadLine();