Let p be a prime number, and let 𝔹_p,n be the nth layer in the cyclotomic ℤ_p-extension of ℚ with ring of integers [Formula: see text]. In this paper we show that for each even integer m ≥ 2 and each prime number p the orders of the Quillen K-groups [Formula: see text] are unbounded, and that there are in fact infinitely many different prime numbers dividing the order of [Formula: see text] for some n.