The question is how it can prove a lower bound for the factors of a
number. I imagine this would be easy for numbers such as repunits
where factors are restricted to special forms, but for other numbers
it might not work very well because of the astonishing number of
For example, for the repunits R311 (not to be confused with R317),
R509 and R557 - the status of which is "Composite But No Factor
Known", this method seems very promising because what I once read
about repunits suggests that these numbers must have two very large
factors and if primality tests for numbers of the correct form are
available, it might solve the problem well, especially for R311,
which mystified me on seeing it in a table of repunits.
The problem is with how to test the primality of the numbers of the
appropriate form - though the effect of not doing this is most likely
to be mere wastage of time ratehr than errors - for instance with the
large 1187-digit cofactor of F12.