PAUL2 - A conjecture of Paul Erdős (hard)
In number theory there is a very deep unsolved conjecture of the Hungarian Paul Erdős (1913-1996), that there exist infinitely many primes of the form x2+1, where x is an integer. However, a weaker form of this conjecture has been proved: there are infinitely many primes of the form x2+y4. You don't need to prove this, it is only your task to find the number of (positive) primes not larger than n which are of the form x2+y4 (where x and y are integers).
An integer T, denoting the number of testcases (T≤500000). Each of the T following lines contains a positive integer n, where n≤1012.
Output the answer for each n.
Input: 6 1 2 10 9999999 500000000000 1000000000000
Output: 0 1 2 13175 25874902 42377120
ps. my running time on Cube is 9.83 seconds. There is one input set.
For a much easier version of this problem see http://www.spoj.com/problems/HS08PAUL.