public static bool SatisfiesConjecture(long n, SortedSet <long> primes, SortedSet <long> twiceSquares)
{
while (primes.Max < n)
{
primes.Add(PrimeUtils.NextPrime(primes));
}
while (twiceSquares.Max < n)
{
twiceSquares.Add(2 * (long)Math.Pow(twiceSquares.Count, 2));
}
return(primes.Any(p => twiceSquares.Contains(n - p)));
}
private void IncreaseBitSetCapacity(Int32 count)
{
Int32 size = PrimeUtils.NextPrime(count);
if (size > _freeIdSize)
{
size = _freeIdSize;
}
BitSet newBitSet = new BitSet(size);
newBitSet.Or(_freeIds);
_freeIds = newBitSet;
}
public Boolean Initialize()
{
try
{
_freeIds = new BitSet(PrimeUtils.NextPrime(100000));
_freeIds.Clear();
_freeIdCount = _freeIdSize;
foreach (UInt32 usedObjectId in ExtractUsedObjectIdTable())
{
if (_exclude.Contains(usedObjectId))
{
continue;
}
Int32 objectId = (Int32)(usedObjectId - _firstId);
if (usedObjectId < _firstId)
{
#if NLOG
_log.Warn("{0}: Object ID {1} in DB is less than {2}", _name, usedObjectId, _firstId);
#endif
continue;
}
if (objectId >= _freeIds.Count)
{
IncreaseBitSetCapacity(objectId + 1);
}
_freeIds.Set(objectId);
Interlocked.Decrement(ref _freeIdCount);
}
_nextFreeId = _freeIds.NextClear(0);
#if NLOG
_log.Info("{0} successfully initialized", _name);
#endif
}
catch (Exception e)
{
#if NLOG
_log.Error("{0} could not be initialized correctly", _name);
_log.Error(e);
#endif
return(false);
}
return(true);
}
public static IEnumerable <long[]> Main()
{
var primes = new SortedSet <long> {
2, 3, 5, 7
};
var primesTodo = new SortedSet <long>();
var digits = 2;
while (true)
{
var maxForDigits = Math.Pow(10, digits);
while (primes.Max < maxForDigits)
{
var nxt = PrimeUtils.NextPrime(primes);
if (nxt >= maxForDigits)
{
break;
}
primes.Add(nxt);
primesTodo.Add(nxt);
}
while (primesTodo.Any())
{
var todo = primesTodo.First();
foreach (var family in Replacements(todo))
{
var familyPrimes = family.Where(x => primes.Contains(x)).ToArray();
yield return(familyPrimes);
primesTodo.ExceptWith(familyPrimes);
}
}
digits++;
}
}
public static long Main(int distinctCount)
{
var primes = new List <long> {
2
};
var count = 0;
var n = 2L;
while (count != distinctCount)
{
if (primes.Last() < n)
{
primes.Add(PrimeUtils.NextPrime(primes));
}
// stop collecting factors if more than distinct count
var primeFactors = GetPrimeFactors(n, primes).TakeWhile((x, i) => i <= distinctCount);
count = primeFactors.Count() == distinctCount ? count + 1 : 0;
n++;
}
return(n - distinctCount);
}
