public void PrimeSieveOfEratosthenes_BigInteger_ReturnsPrimes()
{
var value = 449243;
var result = PrimeUtility.PrimeSieveOfEratosthenes(449244);
Assert.AreEqual(value, result.Last());
}
public void CalculateLargestPrimeFactor()
{
List <double> results = new List <double>();
double remainder = GoalNumber;
// Process
NumericSources.YieldNextPrime().TakeWhile(x => ProcessNumber(x) && x < remainder / 2).ToList();
// Potentially recursively check a single number if it's a factor
bool ProcessNumber(double i)
{
while (IsFactor(i))
{
AdjustRemainder(i);
results.Add(i);
// Once the remainder is a prime, stop.
if (PrimeUtility.IsNumberPrime(remainder))
{
results.Add(remainder);
MaxPrimeOrFactor = remainder;
return(false);
}
}
return(true);
}
bool IsFactor(double i) => remainder % i == 0;
void AdjustRemainder(double i) => remainder = remainder / i;
}
public void LargestPrimeTestCaseorNEW_Integers_ReturnsResult(long n, long value)
{
var p = PrimeUtility.PrimeSieveOfEratosthenes((int)Math.Sqrt(n));
var result = PrimeUtility.LargestPrimeFactorUsingSieve(n, p);
Assert.AreEqual(value, result);
}
public static long GeneralizedSolution(int n)
{
var primes = PrimeUtility.PrimeSieveOfEratosthenes(n);
long sum = primes.Select(x => (long)x).Sum();
return(sum);
}
private static List <long> ReturnLargestPrimeFactors(long n)
{
var summand = new List <long>();
for (long i = 2; i <= n; i++)
{
summand.Add(PrimeUtility.LargestPrimeFactor(i));
}
return(summand);
}
public static long Solution()
{
// see links:
// https://en.wikipedia.org/wiki/Prime_number_theorem#Approximations_for_the_nth_prime_number
// https://math.stackexchange.com/questions/1270814/bounds-for-n-th-prime
const long n = 10001;
const int N = 114319; // n*(log(n) + log(log(n)))
var primes = PrimeUtility.PrimeSieveOfEratosthenes(N);
return(primes[(int)(n - 1)]);
}
public void PrimeSieveOfEratosthenes_Integer_ReturnsPrimes()
{
var primes = new List <int>()
{
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59,
61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127,
131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191,
193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257,
263, 269, 271
};
var result = PrimeUtility.PrimeSieveOfEratosthenes(271);
Assert.AreEqual(primes, result);
}
public static int Solution(int max)
{
var primes = PrimeUtility.PrimeSieveOfEratosthenes(max).ToArray();
for (int i = 9; i <= max; i += 2)
{
if (!i.IsPrime())
{
if (!IsSumOfPrimeAndTwiceSquare(i))
{
return(i);
}
}
}
return(-1);
}
public static bool IsSumOfPrimeAndTwiceSquare(int n)
{
var primes = PrimeUtility.PrimeSieveOfEratosthenes(n);
foreach (var prime in primes)
{
for (int i = 1; i <= n; i++)
{
var condition = prime + 2 * i * i == n;
if (condition)
{
return(true);
}
}
}
return(false);
}
public static int GeneralizedSolution(int size, int max)
{
var primes = PrimeUtility.PrimeSieveOfEratosthenes(max);
foreach (var p in primes)
{
var digitReplacementCombinations = DigitReplacementCombinations(p);
foreach (var combination in digitReplacementCombinations)
{
var numberFamily = DigitReplacementFamily(p, combination.ToArray());
var primeFamily = numberFamily.Where(x => x.IsPrime());
if (primeFamily.Count() == size)
{
return(primeFamily.First());
}
}
}
return(0);
}
public static long SolutionForArbitraryInputUsingSieve(long n)
{
var m = (int)Math.Sqrt(n);
var p = PrimeUtility.PrimeSieveOfEratosthenes(m);
/*var summand = new List<long>();
*
* for (long i = 2; i <= n; i++)
* {
* summand.Add(PrimeUtility.LargestPrimeFactorUsingSieve(i, p));
* }
*
* return summand.Sum();*/
long sum = 0;
for (long i = 2; i <= n; i++)
{
sum += PrimeUtility.LargestPrimeFactorUsingSieve(i, p);
}
return(sum);
}
private static bool IsTripletCondition(int m, int n)
{
return((m - n) % 2 == 1 && // difference is odd
!(m % 2 == 1 && n % 2 == 1) && // both not odd
PrimeUtility.GreatestCommonDivisor(m, n) == 1); // co-prime
}
public static long Solution()
{
return(PrimeUtility.LargestPrimeFactor(600851475143));
}
public void LargestPrimeFactor_Integers_ReturnsResult(long n, long value)
{
var result = PrimeUtility.LargestPrimeFactor(n);
Assert.AreEqual(value, result);
}
public void GreatestCommonDivisor_Integers_ReturnsResult(BigInteger a, BigInteger b, BigInteger value)
{
var result = PrimeUtility.GreatestCommonDivisor(a, b);
Assert.AreEqual(value, result);
}
public void PrimeSieveOfEratosthenes_Integers_ReturnsPrimes(int x, int y)
{
var result = PrimeUtility.PrimeSieveOfEratosthenes(x);
Assert.AreEqual(y, result.Last());
}
