A triple Mertens evaluation

We prove the following triple Mertens evaluation∑pqr≤x,p,q,r prime1pqr=(ln⁡(ln⁡x)+B)3−π22(ln⁡(ln⁡x)+B)+2ζ(3)+O(ln2⁡(ln⁡x)ln⁡x) where B is the Mertens constant and ζ is the Riemann zeta function.