NumberHelpers - Fibonacci Sequence, Primes, IsPrime, Triangles and Pythagoreans

NumberHelpers.cs

using System;
using System.Collections.Generic;

public static class NumberHelpers
{
    /// <summary>
    /// Returns a sequence of fibonacci numbers.
    /// </summary>
    /// <returns></returns>
    public static IEnumerable<long> Fibonacci()
    {
        long n = 0, m = 1, tmp = 0;

        yield return 0;
        yield return 1;
        while (true)
        {
            tmp = n + m;
            n = m;
            m = tmp;
            yield return m;
        }
    }

    /// <summary>
    /// Returns a sequence of factors for a given number.
    /// </summary>
    /// <param name="num">The num.</param>
    /// <returns></returns>
    public static IEnumerable<long> Factors(long num)
    {
        for (long i = 2; i * i <= num; i++)
        {
            if (num % i != 0)
                continue;

            yield return i;
            if (i != i * i)
            {
                yield return (num / i);
            }
        }
    }

    /// <summary>
    /// Returns a sequence of prime numbers.
    /// </summary>
    /// <param name="num">The num to start at.</param>
    /// <returns></returns>
    public static IEnumerable<long> Primes(long num = 2)
    {
        var i = num < 2 ? 2 : num;
        while (true)
        {
            if (IsPrime(i))
                yield return i;

            i++;
        }
    }

    /// <summary>
    /// A Pythagorean is a set of 3 numbers such that a &lt; b &lt; c and a^2 + b^2 = c^2
    /// </summary>
    /// <param name="max">The max a value.</param>
    /// <returns>The sequence of pythagoreans to a given max</returns>
    public static IEnumerable<Tuple<long, long, long>> Pythogoreans(long max)
    {

        for (long i = 1; i < max - 2; i++)
        {
            for (var j = i + 1; j < max - 1; j++)
            {
                for (var k = j + 1; k < max; k++)
                {
                    if ((i * i) + (j * j) == k * k)
                    {
                        yield return Tuple.Create(i, j, k);
                    }
                }
            }
        }
    }

    /// <summary>
    /// A triangle is a sum of all consecutive numbers from 0; e.g. Triangle(5) = 1 + 2 + 3 + 4 + 5 = 15            /// 
    /// </summary>
    /// <returns></returns>
    public static IEnumerable<long> Triangles()
    {
        long i = 1;
        long last = 0;
        while (true)
        {
            yield return last + i;
            last = last + i;
            i++;
        }
    }

    /// <summary>
    /// Weird sequence from Euler problem 14.
    /// </summary>
    /// <param name="start">The start.</param>
    /// <returns></returns>
    public static IEnumerable<long> Euler14Sequence(long start)
    {
        long curr = start;

        yield return curr;

        while (curr != 1)
        {
            if (curr % 2 == 0)
            {
                curr /= 2;
            }
            else
            {
                curr = (3 * curr) + 1;
            }

            yield return curr;
        }
    }

    public static bool IsPrime(long num)
    {
        for (long i = 2; i * i <= num; i++)
        {
            if (num % i != 0)
                continue;

            return false;
        }

        return true;
    }
}