+A number consisting entirely of ones is called a repunit. We shall define R(k)
+to be a repunit of length k; for example, R(6) = 111111.
+Let us consider repunits of the form R(10n).
+Although R(10), R(100), or R(1000) are not divisible by 17, R(10000) is
+divisible by 17. Yet there is no value of n for which R(10n) will divide by 19.
+In fact, it is remarkable that 11, 17, 41, and 73 are the only four primes
+below one-hundred that can be a factor of R(10n).
+Find the sum of all the primes below one-hundred thousand that will never be a
+ $mod = (($mod * 10 + 1) % $n);
+ while (($A & 0x1) == 0)
+open my $primes_fh, "(echo 3 ; primes 7 100000)|";
+# 2 and 5 are such primes and calc_A() will get stuck for them.
+while (my $line = <$primes_fh>)