public static (int, int) GetCoefficientsForQuadraticExpressionWhichProducesMaximumNumberOfPrimes(int maxModulusOfCoefficients)
{
var longestSequenceOfPrimes = 0;
var coefficientsForLongestSequence = (0, 0);
foreach (int a in Enumerable.Range(-maxModulusOfCoefficients + 1, 2 * maxModulusOfCoefficients - 2))
{
foreach (int b in Enumerable.Range(1, maxModulusOfCoefficients))
{
var quadraticFormula = GetQuadraticFormule(a, b);
var n = 0;
while (PrimeHelper.IsPrime(quadraticFormula(n)))
{
n++;
}
if (n > longestSequenceOfPrimes)
{
longestSequenceOfPrimes = n;
coefficientsForLongestSequence = (a, b);
}
}
}
return(coefficientsForLongestSequence);
}
public static long GetLengthOfNumberSpiralForWhichPercentageOfPrimesOnDiagonalsIsLowerThanLimit(int desiredUpperBoundPercentagePrimes)
{
var numberOfDiagonalNumbers = 5;
var numberOfPrimesOnDiagonals = 3;
int increment = 2;
int currentPosition = 9;
while (!(numberOfPrimesOnDiagonals * 100 <= numberOfDiagonalNumbers * desiredUpperBoundPercentagePrimes))
{
increment += 2;
// The odd squares lie on the bottom right diagonal, so these cannot be prime.
for (int i = 0; i < 3; i++)
{
currentPosition += increment;
if (PrimeHelper.IsPrime(currentPosition))
{
numberOfPrimesOnDiagonals++;
}
}
currentPosition += increment;
numberOfDiagonalNumbers += 4;
}
return(increment + 1);
}
private static List <long> GetPandigitalPrimes(List <char> characterAllowedTouse)
{
return(GetPandigitalNumbers(characterAllowedTouse)
.Select(number => long.Parse(number)).Where(number => PrimeHelper.IsPrime(number)).ToList());
}