Sums of squares of primes

The sequence $f(n)$ given by those smallest integers which can be written in $n$ ways as the sum of squares of three primes has first eleven values,

$$12,219,363,699,1179,2019,2259,3891,4059,6459,5379.$$

As one can see, the $10$th value, $6459$, is larger than the $11$th value, $5379$. This is OEIS A214512, which indicates that it was really T.D. Noe who observed this earlier.

In any case it will be some time before this puzzle can be used like this again.

the answer is 2019

$$2019=a^2+b^2+c^2,\;\;\text{with}\;\;(a,b,c)\in\{(7,11,43),(7,17,41),(13,13,41),(11,23,37),(17,19,37),(23,23,31)\}.$$

I think this was first noticed by Ed Southall