%0 Journal Article %T Sums of four squares of primes %A Angel V. Kumchev %A Lilu Zhao %J Mathematics %D 2015 %I arXiv %X Let $E(N)$ denote the number of positive integers $n \le N$, with $n \equiv 4 \pmod{24}$, which cannot be represented as the sum of four squares of primes. We establish that $E(N)\ll N^{11/32}$, thus improving on an earlier result of Harman and the first author, where the exponent $7/20$ appears in place of $11/32$. %U http://arxiv.org/abs/1503.01799v1