On a Lower Bound for $\|(4/3)^k\|$

Abstract

We prove, thatwhere • is a distance to the nearest prime.

Errata and Addenda to Mathematical Constants

“…Zudilin [410] improved Habsieger's lower bound on (3/2) n mod 1, progressing from 0.577 n to 0.5803 n , and similarly obtained estimates for (4/3) n mod 1 when n is suitably large. Concerning the latter, Pupyrev [411,412] obtained (4/9) n for every n ≥ 2, an important achievement. Concerning the former, our desired bound (3/4) n for every n ≥ 8 seems out-of-reach.…”