sr5sieve is indeed the program used to search for FACTORS of the list of candidates to test for primes.
Whenever you find a factor, you know a number is not prime, therefor you need not test it for primality anymore. (Saving time on that of course)
5866607967677  131848*5^11310271
means that the number 131848*5^11310271 has a factor 5866607967677.
Thus that number isn't prime.
In short, your data will be used to shorten the list of candidates to test for primality. The less candidates to test, the better.
