20191016, 11:34  #12 
Nov 2005
101 Posts 
There are some improvements to Fermat's method.
See https://en.wikipedia.org/wiki/Fermat...ization_method > Sieve improvement. You can really cut down the candidates to check by applying a modulo argument. For primes this argument can be applied multiple times. For each mod prime number argument it halves the number of numbers "x" to check. The product of the first 52 primes is ~ 10^98. Since you can not store or iterate efficiently over all the possible candidates you can not do this for the first 52 primes, you might only seedup by using the first  lets say 8  primes which gives a speedup of 2^8 = 256. Also checking if the number is a square can be speed up by applying a mod argument. Doing it for a power of 2 filters out most of the number to check. Last fiddled with by ThiloHarich on 20191016 at 12:09 
20191016, 13:44  #13  
Bamboozled!
"πΊππ·π·π"
May 2003
Down not across
24626_{8} Posts 
Quote:


20191016, 13:53  #14  
"Ben"
Feb 2007
2^{2}·23·37 Posts 
Quote:


20191016, 14:31  #15  
Nov 2005
65_{16} Posts 
Quote:
Ahh you check 10^14 a = sqrt(n) + a' in the area sqrt(n) in 1 hour > quite impressive. Last fiddled with by ThiloHarich on 20191016 at 14:45 

20191016, 15:58  #16 
Sep 2009
2^{2}·3·13^{2} Posts 

20191017, 03:39  #17  
Romulan Interpreter
Jun 2011
Thailand
3×5^{5} Posts 
Quote:
However, there will be 10 cores used for it, each running at 4 GHz, and it also has 4 (four) fast memory channels (x99 i76950x), and a LOT of cache memory, compared to other CPUs, which gives it about 2030% more speed when HT is used (20 threads). Therefore, ~5.5 days times 24 hours, times 10 cores, times 4 GHz, is about 5280 "CPU Hours", more or less... So,... yeah... Edit: @OP, I edited first post of the thread to put the long number in code tags. Please use code tags for long lines without breaks  such long lines make the thread very difficult to read on narrow screens because the size of the browser is extended out of the screen. Edit 2: related to the puzzle itself (we just clicked the link), is there any way to exploit the "terrain difficulty" and "additional hint"? You have the most significant part of the coordinates, which puts you in a "about" 100km large square, and you are looking for something situated on easy terrain (not a mountain, for example), on the south east face (so, it has faces/sides!) at few feet up (so, it has an "up", or "uphill", or is something "floating" above the ground, etc). I have no idea where the place is, and no time for digging deep, I also never participated in the challenge, and I may be talking stupidities, but maybe a perspicacious person could squeeze in the box without factoring the C200? There is also the observation they made that there may be more than 2 factors, so it may be deliberate to point to ECM. Last fiddled with by LaurV on 20191017 at 04:02 

20191017, 12:57  #18 
"Patrick Poitras"
Oct 2019
66_{8} Posts 
At the risk of running this thread offtopic, that graph is really good, and I'd like to read more about the methodology behind it.

20191018, 03:52  #19 
Romulan Interpreter
Jun 2011
Thailand
3×5^{5} Posts 
We did about 10^10 rho iterations with few random bases each, with x^21. Came back empty. So, it is "solid" from this pov.

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