The curvature of the primes was introduced by Rényi in 1950 as a quantitative measure for sign changes in the sequence pn pn+2 - (pn+1)2 where (pn) is the sequence of primes in ascending order. In this talk we shall examine subsequences of the primes that are only moderately dense, and give estimates for their curvature of strength sufficient to exhibit oscillations in distribution of triplets in the sequence examined. This is joint work with C. Elsholtz.