Question

I was trying to solve a problem on SPOJ. We are required to calculate the nth twin prime pair( primes differing by 2). n can be as large as 10^5. I tried a precalculation using a sieve, I had to sieve up to 10^8 to get the maximum n twin prime, but the time limit is strict(2s) and it times out. I noticed people have solved it in 0.00 seconds, so i looked around for a formula on google, and couldnt get anything helpful. Could someone please guide me?

Thanks in advance!!

Answer 1

So basically, sieving up to 20,000,000 is enough, according to Wolfram Alpha. Use plain sieve of Eratosthenes, on odds, with vector<bool> in C++ (what language were you using BTW?).

Track the twin primes right inside the sieve loop. Store the lower prime of a pair in a separate vector as you find the twins, and if an out-of-order (smaller then previous) index is requested (and they are, contrary to the examples shown on the description page), just get the prime from this storage:

size_t n = 10000000, itop=2236;
vector<bool> s;
vector<int> twins;
s.resize(n, true);
int cnt, k1, k2, p1=3, p2, k=0;
cin >> cnt;
if( cnt-- > 0 )
{
    cin >> k1;
    for( size_t i=1; i < n; ++i )  // p=2i+1
    {
        if( s[i] )
        {
            p2 = 2*i+1;
            if( p2-p1 == 2 ) { ++k; twins.push_back(p1); }
            if( k==k1 )
            { 
                cout << p1 << " " << p2 << endl;
                ......

etc. Got accept with 1.05 sec (0.18 sec on Ideone). Or untangle the logic – just pre-calculate 100,000 twin prime pairs right away, and access them in a separate loop afterwards (0.94 sec).