20080325, 16:19  #188  
May 2007
Kansas; USA
5×2,017 Posts 
Quote:
I did miss one of these...125. But 25 and 625 have no algebraic factors because they are powers of 2 that are not divisible by 3. For those k's, n's that are divisible by 2 would have been sieved out with a trivial factor of 3. Here's the rule for k=q^2 that will contain algebraic factors after normal sieving: k=q^2 and q==(3 mod 6); i.e. q=3, 9, 15, etc. or k=9, 81, 225, etc. There is no easy rule that I am aware of for k=q^3, k=q^5, k=q^7, k=q^11, etc. for all prime powers of q. The considerations for k=q^3 and k=q^5 for k<1000 are: k=q^3: k=27, n's divisible by 3 were removed. k=125, missed. k=343, all n divisible by 3 have trivial factors of 3,5,&13 and were sieved out. (Technically I was lucky here because I had not considered this one either.) k=729, all n divisible by 3 have a trivial factor of 7 and were sieved out. (Since this is also a perfect square, all n divisible by 2 were removed.) k=q^5: k=243, n's divisible by 5 were removed. Since we're testing by kvalue, whomever reserves k=125 can remove all n's divisible by 3 from their sieved file. As a general rule, algebraic factors are < 5% of the file so it would only make a nominal difference. Gary Last fiddled with by gd_barnes on 20080325 at 16:26 

20080325, 16:31  #189 
A Sunny Moo
Aug 2007
USA (GMT5)
3·2,083 Posts 
Okay, guys, files are now available for LLRing!
The Doublecheck Drive #1 thread is here. Enjoy! Note: I will unstick and lock this thread soon. All further discussion of this doublecheck effort can be done in the aforementioned thread. Last fiddled with by mdettweiler on 20080325 at 16:31 
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