I develop the idea that time perception is the quantum counterpartto time measurement. Phase-locking and prime number theory wereproposed as the unifying concepts for understanding the optimalsynchronization of clocks and their 1/f frequency noise. Timeperception is shown to depend on the thermodynamics of a quantumalgebra of number and phase operators already proposed for quantumcomputational tasks, and to evolve according to a Hamiltonianmimicking Fechner's law. The mathematics is Bost and Connesquantum model for prime numbers. The picture that emerges is aunique perception state above a critical temperature and plenty ofthem allowed below, which are parametrized by the symmetry groupfor the primitive roots of unity. Squeezing of phase fluctuationsclose to the phase transition temperature may play a role inmemory encoding and conscious activity.