As a very "rough" rule of thumb, I simply divide the N value that is tested by 3.322 to find the number of digits approximately. It seems to work quite nicely due to the nature of 2^n in the formula (value increases 1 digit for each 2^3.322~).

When I am not after exact number of digits, but looking for just an idea on what range I am crunching, I simply multiply N with three and drop the last digit (I find it easier to do, it doesn't matter for me to be a few percentages off unless it really turns out to be prime).


44131: 995972 / 3.322 => 299811 (real one is 299823 digits)
46157: 698207 / 3.322 => 210177 (real one is 210186 digits)
65567: 1013803 / 3.322 => 305179 (real one is 305190 digits)
69109: 1157446 / 3.322 => 348418 (real one is 348431 digits)
54767: 1337287 / 3.322 => 402555 (real one is 402569 digits)

For those interested in GIMPS, this works there as well. Forexample;

13466917 / 3.322 => 4053858 (real one is 4053946 digits)
or;
13.5 million * 3/10 => 4.05 million.