Oscillation conjecture for the Hardy–Littlewood prime-counting inequality
Let x≥2x\geq 2x≥2 be large, let r>0r>0r>0 be real, and set y=logrxy=\log^r xy=logrx. With π(t)=#{p≤t:p is prime}\pi(t)=\#\{p\leq t:p\text{ is prime}\}π(t)=#{p≤t:p is prime}, the oscillation conjecture. Both inequalities … and … occur infinite…