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

primes.

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.