20090727, 15:36  #1 
Account Deleted
"Tim Sorbera"
Aug 2006
San Antonio, TX USA
17·251 Posts 
optimal B1
Which is more efficient: running ECM with a few large B1 increments, (e.g. run some curves at B1=11e3, then more at 5e4, then ...) or incrementing B1 by some optimized amount for each curve? What gives the best optimization for how quickly the minimum expected factor size can grow?
Granular B1 increments are certainly more convenient for communicating and calculating work done (it's certainly easier to say, "I've run 2000 curves at B1=11e6" and to calculate the level from that than if it was incremented), but are they more efficient? 
20090727, 15:58  #2  
Nov 2003
2^{6}×113 Posts 
Quote:
It answers these kinds of questions (and more). 

20090727, 17:04  #3 
Account Deleted
"Tim Sorbera"
Aug 2006
San Antonio, TX USA
1000010101011_{2} Posts 

20090727, 18:26  #4  
Nov 2003
2^{6}·113 Posts 
Quote:
http://cat.inist.fr/?aModele=afficheN&cpsidt=3769506 You can get a copy from the AMS website, but as they own the copyright, it costs $$$..... 

20110527, 12:19  #5  
Nov 2006
Terra
116_{8} Posts 
key paper from 1993
Quote:
Robert D. Silverman; Samuel S. Wagstaff Math. Comp. 61 (1993), 445462 in .pdf is available free from : http://www.ams.org/journals/mcom/199...99311220787/ 

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