Advantage of lattice sieve over line sieve

[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 special-q (p<q and number of special-q'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.

[xilman]

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 special-q (p<q and number of special-q'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 special-q the number is more likely to be smooth.

[chris2be8]

There's a discussion at http://mersenneforum.org/showthread.php?t=2524

Chris

[binu]

Thanks. But I am implementing the lattice sieve proposed by J. M. Pollard, where special-q's are taken as medium primes (B_0<q<B_1; B_1 being the bound on the factor base primes and B_0 varies between 0.1-0.5 fraction of B_1). Then we sieve for EVERY q in that range. Instead if we line sieve for all primes <B_1 (where every prime is used only once) and then report the smooth candidates, won't it consume less time? It is not clear to me. I need help.