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 GetSolutionOfProblem49()
{
var arithmeticSequences = PrimeHelper.ArithmeticPrimePermutationsWith4Digits();
var sequenceWeAreLookingFor = arithmeticSequences[arithmeticSequences.Keys.ToList().Where(number => number != 1487).Single()];
return(long.Parse(sequenceWeAreLookingFor[0].ToString() + sequenceWeAreLookingFor[1].ToString() + sequenceWeAreLookingFor[2].ToString()));
}
public static long GetSolutionOfProblem47()
{
var consecutiveNumbers = 4;
var numberOfDistinctPrimeFactors = 4;
return(PrimeHelper.GetFirstNumberOfConsecutiveNumbersToHaveMDistinctPrimeFactors(consecutiveNumbers, numberOfDistinctPrimeFactors));
}
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);
}
public static int GetNumberOfDivisors(long n)
{
var numberOfDivisors = 1;
var primeFactorization = PrimeHelper.GetPrimeFactorization(n);
foreach (int key in primeFactorization.Keys)
{
numberOfDivisors *= primeFactorization[key] + 1;
}
return(numberOfDivisors);
}
public static (int, int) ToLowestTerms(int numerator, int denominator)
{
var primeFactorizationNumerator = PrimeHelper.GetPrimeFactors(numerator);
var primeFactorizationDenominator = PrimeHelper.GetPrimeFactors(denominator);
var commonPrimes = primeFactorizationNumerator.Where(prime => primeFactorizationDenominator.Remove(prime));
foreach (int prime in commonPrimes)
{
numerator /= prime;
denominator /= prime;
}
return(numerator, denominator);
}
public static long GetSolutionOfProblem37()
{
return(PrimeHelper.GetAllTruncatablePrimes().Sum());
}
public static long GetSolutionOfProblem35()
{
var max = 1000000;
return(PrimeHelper.GetListOfCircularPrimesBelowMax(max).Count());
}
public static long GetSolutionOfProblem97()
{
return(PrimeHelper.LastTenDigitsOfMassiveNonMersennePrimeProblem97());
}
public static long GetSolutionOfProblem69()
{
var max = 1000000;
return(PrimeHelper.HighestProductOfFirstPrimesBelowMax(max));
}
public static long GetSolutionOfProblem51()
{
var desiredSizeOfFamily = 8;
return(PrimeHelper.FirstPrimeWhichHasDesiredSizeOfFamilyByReplacingSomeDigitsBySameNumber(desiredSizeOfFamily));
}
public static long GetSolutionOfProblem50()
{
var max = 1000000;
return(PrimeHelper.PrimeBelowMaxWhichCanBeWrittenAsSumOfMostConsectivePrimes(max));
}
public static long GetSolutionOfProblem46()
{
return(PrimeHelper.GetFirstCounterExampleGoldbachsOtherConjecture());
}
private static List <long> GetPandigitalPrimes(List <char> characterAllowedTouse)
{
return(GetPandigitalNumbers(characterAllowedTouse)
.Select(number => long.Parse(number)).Where(number => PrimeHelper.IsPrime(number)).ToList());
}