20200205, 11:22  #23 
Jun 2003
123D_{16} Posts 

20200205, 13:38  #24 
Nov 2003
2^{2}·5·373 Posts 
Which is what I said. I did not specify a particular method.

20200205, 14:45  #25 
Bamboozled!
May 2003
Down not across
7×1,453 Posts 

20200205, 14:45  #26 
6809 > 6502
"""""""""""""""""""
Aug 2003
101×103 Posts
47×179 Posts 
And for the OP's benefit they are actually showing real world examples to demonstrate this. No need to get your knickers in a knot. You should be thanking them for demonstrating this conclusively to the OP.

20200205, 15:27  #27  
Romulan Interpreter
Jun 2011
Thailand
10000110111011_{2} Posts 
Quote:
Better lock this topic before sparks get to flames... The OP got his answer already. Last fiddled with by LaurV on 20200205 at 15:31 

20200206, 03:55  #28  
Aug 2006
2·7·419 Posts 
Quote:


20200206, 04:26  #29 
Romulan Interpreter
Jun 2011
Thailand
8635_{10} Posts 
That is easy, because I got recently into a PM exchange with Hans Loeblich who extended my script for more classes and made it faster and parallel, and that is easy to find, I try to keep my PM list in order hehe... All the links are there, in that thread (edit2: posts from #32 to #52 and after, the script is attached to post #52  interesting that the examples provided there were exactly for M67, haha)
Edit: I reopened the topic, as long as the argument continues , it didn't feel right that only the mods can post, and other users have to right to reply if they choose so. Last fiddled with by LaurV on 20200207 at 08:51 
20200206, 21:07  #30 
Aug 2006
2·7·419 Posts 
Thank you.
By the way, why 420 instead of 210? 
20200207, 03:05  #31 
Jun 2003
7·23·29 Posts 
There are two classes, 1 and 7 (mod 8)
Last fiddled with by axn on 20200207 at 03:05 
20200207, 05:28  #32 
Romulan Interpreter
Jun 2011
Thailand
5·11·157 Posts 
Because making it multiple of 4 helps a lot when eliminating classes of k which would result in factors q=2kp+1 being 3 and 5 (mod 8). If the number of classes are 4, 12, 60, 420, 4620 (the double primorials, instead of 2, 6, 30, 210, 2310), then for some k and p, will have q already in the right class (mod 8).
For example: if p is 3 (mod 4) and k is 15 (mod 420), therefore k is 3 (mod 4) (here, you could not say that, in case of k in 210 classes! You would have no information about modularity of k to 4, as 210 is not multiple of 4), therefore q is 2*3*3+1=19 (mod 8, due to the 2 in front, you can double the modulus here), which is 3 (mod 8) and so, when p=3 (mod 4), you can completely eliminate the class k=15 (mod 420), due to the fact that all mersenne factors must be 1 or 7 (mod 8). When p=3 (mod 4), there is no factor q=2kp+1 with k=15 (mod 420). This is how you get from 4620 classes to only 960 to test for each p, or respectively, from 420 to only 96. That's why. This doubles the testing speed. See those 3 posts of mine in the linked thread where I explained. The idea is not mine, it comes from Oliver and the forum (there are antique discussions from when he was developing mfaktc, in mfaktc thread and archieves). Last fiddled with by LaurV on 20200207 at 05:58 Reason: grr...hating the multipl empty lines between paragraphs... 
20200207, 06:33  #33 
Aug 2006
2·7·419 Posts 
Thanks!

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