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Problem027.cs
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Problem027.cs
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namespace ProjectEuler.Solutions
{
using NUnit.Framework;
using ProjectEuler.Helper;
/// <summary>
/// Quadratic primes.
/// Euler discovered the remarkable quadratic formula:
/// <para>n<sup>2</sup> + n + 41</para>
/// It turns out that the formula will produce 40 primes for the consecutive values n = 0 to 39.
/// However, when n = 40, 402 + 40 + 41 = 40(40 + 1) + 41 is divisible by 41, and certainly when n = 41, 41² + 41 + 41 is clearly divisible by 41.
/// <para>
/// The incredible formula n² − 79n + 1601 was discovered, which produces 80 primes for the consecutive values n = 0 to 79.
/// The product of the coefficients, −79 and 1601, is −126479.
/// </para>
/// Considering quadratics of the form:
/// <para>n² + an + b, where |a| < 1000 and |b| < 1000</para>
/// where |n| is the modulus/absolute value of n e.g. |11| = 11 and |−4| = 4
/// <para>Find the product of the coefficients, a and b, for the quadratic expression that produces the maximum number of primes for consecutive values of n, starting with n = 0.</para>
/// </summary>
public class Problem027 : Problem
{
public override long Solution()
{
long coefficientsProduct = 0;
int amountConsecutiveValues = 0;
for(int a = -1000; a <= 1000; a++)
{
for(int b = -1000; b <= 1000; b++)
{
int counter = 0;
long value;
do
{
value = GetValue(counter++, a, b);
}
while(Primes.IsPrimeNumber(value));
counter--;
if(counter > amountConsecutiveValues)
{
amountConsecutiveValues = counter;
coefficientsProduct = a * b;
}
}
}
return coefficientsProduct;
}
private static long GetValue(int number, int a, int b)
{
return (number * number) + (a * number) + b;
}
[Test]
public void TestForExample()
{
for(int i = 0; i <= 39; i++)
{
Assert.IsTrue(Primes.IsPrimeNumber(GetValue(i, 1, 41)));
}
Assert.IsFalse(Primes.IsPrimeNumber(GetValue(40, 1, 41)));
}
[Test]
public void TestForProblem()
{
Assert.AreEqual(-59231, this.Solution());
}
}
}