Primo quit with "Candidate is presumably a square"
 

Hi there, I'm hoping someone could help me with Primo. I have a 2368 digit probable prime, but Primo aborts a few seconds into the certification with the status "Candidate is presumably a square". It does not give any indication as to why it is presumably a square.

The number is the least common multiple of all the integers from 1 to 5449, plus 1:
lcm(1, 2, ... 5449) + 1

I have found further terms for the related sequences [url=https://oeis.org/A049536]A049536[/url] and [url=https://oeis.org/A049537]A049537[/url] on OEIS, and wish to prove them prime, Primo however has other plans.

I have uploaded the .in file for anyone who wishes to try it, I have had to add the additional extension .txt to appease the forum, so that will need to be removed first.

Indeed, it does, and indeed it is not a square!
Try the [URL="http://ellipsa.eu/public/primo/primo.html"]linux alpha version[/URL]? It is different and may be free of this bug?

Ah, I was hoping I could just invert the polarity of something in a config file to fix it.

I'm afraid I occupy a Linux free zone. Nevertheless, I have been trying to do something very Linuxy on Windows, which is to say compiling [url=http://sourceforge.net/projects/gmp-ecpp/]GMP-ECPP[/url]. Unfortunately I understand very little of the process and am being prevented from doing so by 2 errors and 2 warnings.

[CODE]/m/ECPP> ./atkin235.gmp-5.0.1
random seed = 1307956510
error_shift = 1000
precision = 10000
total = 3183
max = 111763
PI = 3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214808651328230...

number to be tested:
4651492098832669839577282545688156677339445061279465845249031751238423754923388468675292837260397395471135746890874769...
Bmax = 2000

#-- We are sinking! We are sinking!
#-- Errh... What ...are you 'sinking about?
[/CODE]
(it seems to be thinking about something... we'll see)

A friend on Linux tried the new 4.0.0 alpha 6 version of Primo and got the same error. Would this be worth contacting the developers about?

We also both got quite stuck trying to compile ECPP. How did your build of ECPP do Batalov, did it fail on this number or was it making progress?

It is măil at ęllipšă dot ęü
and Marcel is a very nice guy.

P.S. GMP-ECPP process is still running but I haven't redirected its output so I will not have a certificate - only will tell you if/when it will finish. Primo would have finished by now. I simply built as per the source instructions - a single line, no makefile, prereq: need -lgmpxx (which has the C++ binidings, I gather) and -lgmp.

[url]http://www.youtube.com/watch?v=VSdxqIBfEAw[/url]

My friend on Ubuntu got ECPP compiled (with -o3), and did a test on a small number. Unfortunately, even on a faster CPU, GMP-ECPP was approximately 210 times slower than Primo (2.26 GHz i3 vs 1.7 GHz P4).

I'm not sure if that's normal, it seems a pretty large factor to be slower by. It would turn a few hours of computation into a couple of months. :down:

I've finished a proof for 10^999+7 with ECPP thing, and indeed it is very slow. Primo on the same number took 22 minutes, ECPP took almost 10 hours. The size dependence for both algos should be O(digits[SUP]4+o(1)[/SUP]), so it looks pretty bleak for even a 2700-digit number. Do write to Marcel; he will be happy to fix this small problem, I think.

I did email Marcel, he has now fixed the Linux version. I have inquired further about whether the Windows version will also receive the fix.

And off it goes using four threads if you'd need it... Should be pretty fast.