Quote:
Originally Posted by binu
In line sieve, we sieve for a particular small prime p for only once; and in lattice sieve, we sieve for that p for every specialq (p<q and number of specialq's may be very large). So, what is the gain in the latter one? Definitely, I am missing something. Can anyone please elaborate the gains/advantage of lattice sieve in details, and also on the choice of the parameters C and D.
Thanks in advance.

If you know in advance that a value is divisible by the prime specialq the number is more likely to be smooth.