Quote:
Originally Posted by andi314
but this will only help to tell you that the numbers are NOT PRIME because the primilty tests for such big numbers ( without a suitable form like Mersenne Numbers) will take some hundred years of computing to verify that it is prime

It is partially what we are doing for Mersennes at LMH > 79.2M.
Maybe it is useful to have a table of factored numbers from where someone else will start checking primality.
My hint: avoiding sums wirh numbers of the form 3n+2, as they will always have 3 as a factor will spped up search.
Luigi