20140404, 15:38  #111 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2·3^{3}·13^{2} Posts 
Now you can do that! ;)

20140404, 17:53  #112 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2×3^{3}×13^{2} Posts 
Warning: LLR prefactoring misses some factors.
This is in addition to the known bug that it hangs on some factors that are slightly smaller than 2^32 (has to be killed and restarted; reports a factor "1" and not necessarily for the correct side, i.e. GM/GQ). Examine your logs; each exponent with the reported factor of "1" should be rechecked with PARI ...or reentered into the pool of candidates (or else one can miss a prime/PRP). Examples: Code:
1st kind: 2^4748941+2^2374471+1 has a factor : 1401773408617 [TF:1:62:mfaktc 0.20 75bit_mul32] 2^47708392^2385420+1 has a factor : 15737871942997 [TF:1:62:mfaktc 0.20 75bit_mul32] 2^4772107+2^2386054+1 has a factor : 22894106978789 [TF:1:62:mfaktc 0.20 75bit_mul32] 2^47391432^2369572+1 has a factor : 115378303475689 [TF:1:62:mfaktc 0.20 75bit_mul32] 2^47695932^2384797+1 has a factor : 209112235666913 [TF:1:62:mfaktc 0.20 75bit_mul32] 2nd kind (these are found with PARI/gp): 4766423 4289780701 + /5 4777781 4280891777  /5 4824697 4284330937  4898687 4291249813  4944817 4292101157 + /5 4957219 4283037217  /5 4961477 4286716129 + 4989353 4290843581  5020591 4277543533 + /5 
20140404, 23:09  #113 
Jun 2003
11^{2}×13 Posts 
I looked through my logs. I have not had any case where LLR reports a factor "1". Is this limited to factors <2^32 or on a particular machine/chipset?
If it is limited to <2^32, is it safe to use the file on Jean's website? 
20140405, 00:33  #114 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2·3^{3}·13^{2} Posts 
2nd kind is limited to 2^32 in size. It is probably also confounded to some 32bit emulation problem on 64bit computers (checked on both Win7 64 and linux64); but I cannot check 32bit comps  it's been a while since I've seen one. If you have one, can you check type 1* and type 2 errors as shown above on it?
I've never looked at Jean's file but it looks ok (now that I've looked at it); he must have used a 32bit OS. ______________ *actually, this is easily checked from your LLR_GM file: all five examples of type 1 are retained in it, so the factors were not found. Last fiddled with by Batalov on 20140405 at 00:38 
20140405, 17:47  #116 
Jun 2003
11^{2}·13 Posts 
Congratulations!
I don't completely understand your previous post (with the software bug). Do we need to redo any ranges for a missed prime etc or are we good? 
20140405, 18:24  #117 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2·3^{3}·13^{2} Posts 
The missed factors (1st kind) are not dangerous per se, because they produce false negatives only (a factor is missed), so the candidate lives on, goes through a more computationally expensive N1 test. It is still checked, which is good. We wouldn't even know that a factor exists without gmqfaktc (because these factors are not tiny, too large for PARI).
For the 2nd kind: well, I cannot check a 32bit behavior, but I conjecture (based on Jean's output files) that LLR 32bit sieve works properly on 32bit CPUs, but has rare but reproducible hiccups on the 64bit CPUs. If you ran 32bit LLR only in 32bit setting, you should be fine (and you report that there were no hangups like shown above). However, if you (or LLR in its output files) removes a candidate from N1 testing then there will exist some unchecked candidates that don't really have a factor. When one runs the LLR32 on a 64bit OS, everything mostly runs fine, and then every once in a while LLR says "has factor : 1" and does not output such candidate to the output stream. I run the PARI validation on all factors before removing the candidates. Like this (./validator.pl < factors  gp q): Code:
#!/usr/bin/perl w while(<>) { s/\s+$//; if(/^\(?2\^(\d+)([+])2\^(\d+).*has a factor *: (\d+)/) { print "f=Mod(2,$4);if(f^",$1,$2,"f^",$3,"+1,print(\"NOT $_\"))\n" if $4 > 2; } elsif(/^\(?2\^(\d+)([+]).*has a factor *: (\d+)/) { print "f=Mod(2,$3);if(f^",$1,$2,"f^",($1+1)/2,"+1,print(\"NOT $_\"))\n" if $3 > 2; } } 
20140405, 18:50  #118 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
21646_{8} Posts 
The debug cases
Here is the short test.
Prerequisites: 1. A 32bit LLR binary (you can try various versions) 2. Use this llr.ini Code:
FacTo=48 TestGM=1 TestGQ=0 PgenInputFile=test1.txt PgenOutputFile=out1.txt Code:
ABC4^$a+1 4748941 4770839 4772107 4739143 4769593 4766423 4777781 4824697 4898687 4944817 
20140405, 19:15  #119 
Jun 2003
11^{2}·13 Posts 
On a 64 bit machine running a 32 bit LLR I get the same errors.
On a 32 bit machine running a 32 bit LLR, LLR finds the factors for lines 15 but gets stuck on lines 610. Should we resieve the whole untested range? What % of factors is LLR missing? Does this bug depend on the size of the exponent of the GM/GQ number? None of my sieve files have this error? May be it only occurs in 4.7M+ range? Last fiddled with by Citrix on 20140405 at 19:17 
20140405, 20:21  #120 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
23A6_{16} Posts 
I have seen this bug since the beginning  it is everywhere (not just for p>4.7M; this was just my recent range), but it is understandably patchy (see below). I think there is an overflow and it happens when (1ε)*2^32 < f < 2^32. ε is small.
Now, why is it patchy? Because f = 4kp + 1, and for some ranges of p, there are no f values that enter the dangerous interval (and when some f does, it still needs to be prime, and if it is not, it is silently dismissed without a bug). I've already run an emulation (it is easier done in PARI, because... well, because to find these in LLR, one needs to manually kill the processes multiple times  and it is tedious). So, I have identified all small p for which the bug occurs and rechecked all of them, first for legitimate factors and then with N1. I have done this for my intervals. But I didn't do it recently for other ranges. Last time I ran it was for all p<3M, iirc. This can be repeated, to be safe; this is a nice little DC project for someone: little because there are really very few of these. 
20140406, 00:50  #121  
Jun 2003
11^{2}·13 Posts 
Quote:
The Type II error can be avoided by using the format N GMfactor GQfactor eg) N 1 1 I got the following output on a 64 bit machine. Code:
2^48986872^2449344+1 has a factor : 89391240377 2^49448172^2472409+1 has a factor : 46224149317 LLR is still missing factors (Type I error). I am not sure if I would want to continue doing the painfully long N1 test, if a small factor exists. I would like to find the small factors first. Is there a 64 bit windows binary for gmqfaktc? What is the input format? 

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