public ActionResult Problem41(uint n)
{
if (n > 9)
{
n = 9;
}
// Set up prime calculator
var cal = new PrimeCalculator();
// Keep trying until we run out of digits.
while (n > 0)
{
List <int> digits = Enumerable.Range(1, (int)n).ToList();
var permutations = new Permutations <int>(digits);
var allPrimes = permutations.Select(numList => numList.MakeNumber())
.Where(num => cal.IsPrimeAutoExpand(num)).ToList();
// If there is at least 1 prime with n-digit, find the maximum amongst these primes and
// that's the answer
if (allPrimes.Count > 0)
{
ulong max = allPrimes.Max();
return(ViewAnswer(41, "The maximum " + n + "-digit pandigital prime is", max));
}
// Otherwise, reduce number of digits and try again.
--n;
}
return(ViewAnswer(41, "No n-digit pandigital prime found.", 0));
}
public ActionResult Problem27(uint n)
{
ulong max = 2 * n * n + n; // because n^2 + n*n + n is divisible by n
var cal = new PrimeCalculator((uint)max / 3);
int max_a = 0, max_b = 0, max_i = 0;
int minus_n = (-1 * (int)n) + 1;
for (int a = minus_n; a < n; a++)
{
for (int b = minus_n; b < n; b++)
{
int i;
for (i = 0; i < n; i++)
{
long p = i * i + a * i + b;
if (p <= 0)
{
break;
}
if (!cal.IsPrimeAutoExpand((ulong)p))
{
break;
}
}
if (i > max_i)
{
max_i = i;
max_a = a;
max_b = b;
}
}
}
string s = string.Format("a = {0} b = {1} n = 0..{2} a*b = ", max_a, max_b, max_i);
return(ViewAnswer(27, s, max_a * max_b));
}
public ActionResult Problem50(ulong n)
{
var cal = new PrimeCalculator(40000);
cal.ExtendToMinimumGT(n);
// Cumsums.. cumsum[i] = sum of primes[0 .. i]
var primes = cal.Primes;
var cumsums = primes.CumSum().ToArray();
// Calc sum from [fromPos, toPos]
Func <int, int, ulong> calcSum = (fromPos, toPos) =>
{
int before = fromPos - 1;
if (before >= 0)
{
return(cumsums[toPos] - cumsums[before]);
}
else
{
return(cumsums[toPos]);
}
};
// Find end position for range to examine.
int endPos;
for (endPos = primes.Length - 1; endPos >= 0 && primes[endPos] > n; endPos--)
{
;
}
// Loop through all possible values for [start, end] to find the longest range whose
// sum is still a prime
int maxLen = 0, maxStart = 0;
ulong maxNum = 0;
for (int end = 0; end <= endPos; end++)
{
for (int start = 0; start < end; start++)
{
int len = end - start + 1;
if (len < maxLen)
{
continue;
}
ulong sum = calcSum(start, end);
if (sum > n)
{
continue;
}
if (!cal.IsPrimeAutoExpand(sum))
{
continue;
}
maxLen = len;
maxNum = sum;
maxStart = start;
}
}
int maxEnd = maxStart + maxLen - 1;
ulong maxValue = calcSum(maxStart, maxEnd);
var s = string.Format("{0} + .. + {1} = {2} len = {3}",
primes[maxStart], primes[maxEnd], maxValue, maxEnd, maxLen);
return(ViewAnswer(50, s, maxValue));
}
