Heath-Brown–Moroz constant

The Heath-Brown–Moroz constant C, named for Roger Heath-Brown and Boris Moroz, is defined as


 * $$C=\prod_p\left(1-\frac{1}{p}\right)^7\left(1+\frac{7p+1}{p^2}\right) = 0.001317641... $$

where p runs over the primes.

Application
This constant is part of an asymptotic estimate for the distribution of rational points of bounded height on the cubic surface X03=X1X2X3. Let H be a positive real number and N(H) the number of solutions to the equation X03=X1X2X3 with all the Xi non-negative integers less than or equal to H and their greatest common divisor equal to 1. Then


 * $$N(H)= C \cdot \frac{H(\log H)^6} {4\times 6!} + O(H(\log H)^5)$$.