Bash + GNU utilities, 86 bytes
for((k=4;k<1ドル;k++,j=k-2)){ [ $(factor $k $j|wc -w) = 4 ]&&x=$x+1/$k+1/$j;};bc -l<<<0$x
Constructs a large arithmetic expression and then feeds it to bc -l to evaluate it.
Mitchell Spector
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