20130413, 13:37  #1 
Apr 2013
2 Posts 
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. 
20130413, 14:18  #2  
Bamboozled!
"πΊππ·π·π"
May 2003
Down not across
10,243 Posts 
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20130413, 16:05  #3 
Sep 2009
2^{2}·11·43 Posts 

20130413, 16:32  #4 
Apr 2013
2 Posts 
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. I need help.

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