Transcendence of Mills’ constant under the Riemann hypothesis

Determine whether Mills’ constant ξ₃ is transcendental under the assumption of the Riemann hypothesis.

Background

The authors establish the irrationality of Mills’ constant and provide conditional criteria implying its transcendence. They discuss known results on primes in short intervals under the Riemann hypothesis and observe that current bounds are insufficient to conclude transcendence via their methods.

They therefore explicitly ask whether assuming the Riemann hypothesis is enough to deduce the transcendence of ξ₃, highlighting a conditional open direction beyond their current results.