Advantage of lattice sieve over line sieve
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. 
[QUOTE=binu;336946]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.[/QUOTE]If you know in advance that a value is divisible by the prime specialq the number is more likely to be smooth. 
There's a discussion at [URL]http://mersenneforum.org/showthread.php?t=2524[/URL]
Chris 
Thanks. But I am implementing the lattice sieve proposed by J. M. Pollard, where specialq'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 0.10.5 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. :sad: I need help.

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