private IEnumerable <SideLengthAndRatio> SideLengthAndRatios()
{
var primeCalculate = new Primes(1000000000);
primeCalculate.CalculatePrimes();
var primes = primeCalculate.PrimeList().GetEnumerator();
var numberDiagonals = 1;
var numberPrimes = 0;
for (long length = 3;; length += 2)
{
var corner = length * length;
var step = length - 1;
// create small prime checking set
var primeSet = new HashSet <long>();
while (primes.MoveNext())
{
var next = primes.Current;
if (next > corner)
{
break;
}
primeSet.Add(next);
}
// exclude corner as it is clearly not prime
numberPrimes += new[] { corner - step, corner - step * 2, corner - step * 3 }
.Count(x => primeSet.Contains(x));
numberDiagonals += 4;
yield return(new SideLengthAndRatio(length, numberPrimes, numberDiagonals));
}
}
public string Solve()
{
var p = new Primes(2000000);
p.CalculatePrimes();
long s = p.PrimeList().Select(x => (long)x).Sum();
return(s.ToString());
}
public IEnumerable <int> BruteSolve()
{
var primeCalculator = new Primes(1000000);
var primes = new HashSet <int>(primeCalculator.PrimeList());
return(primes
.Where(IsTruncatableFirstPass)
.Where(x => Truncations(x).All(y => primes.Contains(y))));
}
private IEnumerable <int> PrimesUnder(int n)
{
// add more primes if needed
if (_primesList.LastOrDefault() < n)
{
checked
{
_primes = new Primes(n * n > 100000 ? n * n : 100000);
_primesList = _primes.PrimeList().ToList();
}
}
var i = GetIndexOfLessThanOrEqual(_primesList, n);
return(_primesList.Take(i + 1));
}
public string Solve()
{
var primes = new Primes((int)1e9);
primes.CalculatePrimes();
foreach (var prime in primes.PrimesListBackwards())
{
if (IsPandigital(prime))
{
return(prime.ToString());
}
}
return("");
}
public Tuple <int, int, int> FindPrimeFormula()
{
// one of the largest possible value is 1000*1000 + 1000*1000 + 1000 < 2100000
// with the restrictions given
var primes = new Primes(2100000);
var primesSet = new HashSet <int>(primes.PrimeList());
var abCombinations = from i in Enumerable.Range(-1000, 2000)
from j in Enumerable.Range(-1000, 2000)
select Tuple.Create(i, j);
var answer = abCombinations.Select(n =>
{
var count = QuadraticWith(n.Item1, n.Item2).TakeWhile(primesSet.Contains).Count();
return(Tuple.Create(n.Item1, n.Item2, count));
}).Aggregate((a, b) => a.Item3 > b.Item3 ? a : b);
return(answer);
}
public static int GetEnglishNumberLetterCount(int n)
{
// pad the number to be divisible by three for grouping convenience
var radix = n.ToString();
var addPad = Primes.Mod(-radix.Length, 3);
radix = radix.PadLeft(radix.Length + addPad);
var count = 0;
foreach (var t in radix.SplitUpIntoGroups(3).Enumerate())
{
var i = t.Item1;
var grp = t.Item2;
var numbers = grp.Aggregate("", (prev, next) => prev + next);
count += CountEnglishNumberGroup(Convert.ToInt32(numbers));
count += ThreeDigitSectionNames[(int)i];
}
return(count);
}
private IEnumerable <int> BruteSolve()
{
var primesCalculator = new Primes(1000000);
var primes = new HashSet <int>(primesCalculator.PrimeList());
var circularPrimes = new HashSet <int>();
foreach (var prime in primes)
{
if (circularPrimes.Contains(prime))
{
continue;
}
var rotations = Rotations(prime);
if (rotations.All(x => primes.Contains(x)))
{
rotations.ForEach(rotation => circularPrimes.Add(rotation));
}
}
return(circularPrimes);
}
public string Solve()
{
var primesList = new Primes(1000000).PrimeList().ToArray();
var primes = new HashSet <int>(primesList);
// brute force: check every combination of consecutive primes
var largestStart = 0;
var largestCount = 0;
var largestPrime = 0;
for (var i = 1; i < primesList.Length; i++)
{
var sum = primesList[i];
for (var j = i + 1; j < primesList.Length; j++)
{
sum += primesList[j];
if (sum > 1000000)
{
break;
}
if (j - i > largestCount && primes.Contains(sum))
{
largestStart = i;
largestCount = j - i;
largestPrime = sum;
}
}
if (sum > 1000000)
{
continue;
}
}
return(largestPrime.ToString());
}