bool FirstPrime(Integer &p, const Integer &max, const Integer &equiv, const Integer &mod)
{
assert(!equiv.IsNegative() && equiv < mod);
Integer gcd = GCD(equiv, mod);
if (gcd != Integer::One())
{
// the only possible prime p such that p%mod==equiv where GCD(mod,equiv)!=1 is GCD(mod,equiv)
if (p <= gcd && gcd <= max && IsPrime(gcd))
{
p = gcd;
return true;
}
else
return false;
}
BuildPrimeTable();
if (p <= primeTable[primeTableSize-1])
{
word *pItr;
--p;
if (p.IsPositive())
pItr = std::upper_bound(primeTable, primeTable+primeTableSize, p.ConvertToLong());
else
pItr = primeTable;
while (pItr < primeTable+primeTableSize && *pItr%mod != equiv)
++pItr;
if (pItr < primeTable+primeTableSize)
{
p = *pItr;
return p <= max;
}
p = primeTable[primeTableSize-1]+1;
}
assert(p > primeTable[primeTableSize-1]);
if (mod.IsOdd())
return FirstPrime(p, max, CRT(equiv, mod, 1, 2, 1), mod<<1);
p += (equiv-p)%mod;
if (p>max)
return false;
PrimeSieve sieve(p, max, mod);
while (sieve.NextCandidate(p))
{
if (FastProbablePrimeTest(p) && IsPrime(p))
return true;
}
return false;
}
bool FirstPrime(Integer &p, const Integer &max, const Integer &equiv, const Integer &mod, const PrimeSelector *pSelector)
{
assert(!equiv.IsNegative() && equiv < mod);
Integer gcd = GCD(equiv, mod);
if (gcd != Integer::One())
{
// the only possible prime p such that p%mod==equiv where GCD(mod,equiv)!=1 is GCD(mod,equiv)
if (p <= gcd && gcd <= max && IsPrime(gcd) && (!pSelector || pSelector->IsAcceptable(gcd)))
{
p = gcd;
return true;
}
else
return false;
}
unsigned int primeTableSize;
const word16 * primeTable = GetPrimeTable(primeTableSize);
if (p <= primeTable[primeTableSize-1])
{
const word16 *pItr;
--p;
if (p.IsPositive())
pItr = std::upper_bound(primeTable, primeTable+primeTableSize, (word)p.ConvertToLong());
else
pItr = primeTable;
while (pItr < primeTable+primeTableSize && !(*pItr%mod == equiv && (!pSelector || pSelector->IsAcceptable(*pItr))))
++pItr;
if (pItr < primeTable+primeTableSize)
{
p = *pItr;
return p <= max;
}
p = primeTable[primeTableSize-1]+1;
}
assert(p > primeTable[primeTableSize-1]);
if (mod.IsOdd())
return FirstPrime(p, max, CRT(equiv, mod, 1, 2, 1), mod<<1, pSelector);
p += (equiv-p)%mod;
if (p>max)
return false;
PrimeSieve sieve(p, max, mod);
while (sieve.NextCandidate(p))
{
if ((!pSelector || pSelector->IsAcceptable(p)) && FastProbablePrimeTest(p) && IsPrime(p))
return true;
}
return false;
}