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 2010-12-24, 19:38 #45 Harvey563     Apr 2004 11×17 Posts 3700 - 3799 finished, reserving 3800 - 3899 I have checked 3700 through 3799, had to go to the other side for 3707 and 3732. Taking 3800 through 3899.
 2010-12-31, 14:10 #46 rogue     "Mark" Apr 2003 Between here and the 144508 Posts Conjecture disproven? I believe that I found a k for which no there are no primes, 4169. Could someone please do a double-check for me? Give me some time and I will post sieve files for the multiply and divide side along with the factors for those that have been removed.
 2010-12-31, 15:51 #47 Harvey563     Apr 2004 11×17 Posts double check I am starting a double check now. :surprised
2010-12-31, 16:46   #48
rogue

"Mark"
Apr 2003
Between here and the

23×5×7×23 Posts

Here are the numbers to test on the multiply side. I also included factors found by the sieve, so with a little massaging they can be verified by PFGW.
Attached Files
 mul_4169.zip (40.9 KB, 234 views)

2010-12-31, 18:18   #49
rogue

"Mark"
Apr 2003
Between here and the

23×5×7×23 Posts

And the ones to test on the divide side.
Attached Files
 div_4169.zip (40.9 KB, 239 views)

 2010-12-31, 20:17 #50 Mini-Geek Account Deleted     "Tim Sorbera" Aug 2006 San Antonio, TX USA 3·1,423 Posts I am also running a double check, using an unsieved ABC2 file (below) and -f. Code: ABC2 p(4169)#$ap($b)$c a: in { * / } b: from 1 to 4169 c: in { -1 +1} To anyone double checking: be sure to log the residues for comparison. Last fiddled with by Mini-Geek on 2010-12-31 at 20:47 2010-12-31, 20:46 #51 rogue "Mark" Apr 2003 Between here and the 23·5·7·23 Posts Quote:  Originally Posted by Mini-Geek I am also running a double check, using an unsieved ABC2 file (below) and -f. Code: ABC2 p(4169)#$ap($b)$c a: in { * / } b: from 1 to 4169 c: in { -1 +1}
Interesting. I didn't realize that PFGW could substitute symbols.

2010-12-31, 20:52   #52
Mini-Geek
Account Deleted

"Tim Sorbera"
Aug 2006
San Antonio, TX USA

Quote:
 Originally Posted by rogue Interesting. I didn't realize that PFGW could substitute symbols.
Really? Interesting. Haha. I wasn't sure if it could, especially with it looking like "$ap", so I tried it out, and it looks like it works fine. e.g. here's the start of my pfgw.out: Code: p(4169)#*p(1)-1 has factors: 687151 p(4169)#/p(1)-1 has factors: 2 p(4169)#*p(2)-1 is composite: RES64: [753B916ADC6766D6] (12.8772s+5.0848s) p(4169)#/p(2)-1 is composite: RES64: [F9C25D55CBB51B98] (12.7213s+4.1486s) It also works like this: Code: ABC2 p(4169)#$ap($c)$b1
a: in { * / }
b: in { - + }
c: from 1 to 4169
Making output like:
Code:
p(4169)#*p(1)-1 has factors: 687151
p(4169)#/p(1)-1 has factors: 2
p(4169)#*p(1)+1 is composite: RES64: [3C2718BB83B8ADE0] (12.7991s+5.9587s)
p(4169)#/p(1)+1 has factors: 2^2
p(4169)#*p(2)-1 is composite: RES64: [753B916ADC6766D6] (12.6754s+4.2350s)
If I had noticed that before, I would've done it like that, but it's good enough as is, and too much trouble to change now.
You can also do something like this:
Code:
ABC2 349*2^\$a000-1
a: from 1 to 2
And it tests 349*2^1000-1 and 349*2^2000-1. ABC2 is really quite flexible in what it can put in to the expression.

Last fiddled with by Mini-Geek on 2010-12-31 at 21:15

 2010-12-31, 21:37 #53 rogue     "Mark" Apr 2003 Between here and the 23×5×7×23 Posts I rarely use ABC2 because I have the skills to write a sieve which removes a lot more candidates. In any case, it's nice to know that ABC2 is so powerful. I have wanted to make scripting more powerful by not requiring string input from files to be a valid expression. When I started writing the sieve for this problem, I tried to output j.in like this: "/p(j)+1", but the PFGW script didn't like that unless I removed the "/". Last fiddled with by rogue on 2010-12-31 at 21:41
 2011-01-02, 00:33 #54 Mini-Geek Account Deleted     "Tim Sorbera" Aug 2006 San Antonio, TX USA 3×1,423 Posts I haven't quite finished the double check, (still have to do 3893<=j<=4169 on the plus side) but I'm afraid I've found a few primes: Code: p(4169)#*p(2934)-1 p(4169)#*p(3789)-1 p(4169)#*p(2890)+1 p(4169)#*p(3256)+1 All proven prime. There weren't any false factors for these numbers in your posted files, they were listed as candidates, but I do wonder what mistake (human or computer) made you think the multiply side had no primes. Last fiddled with by Mini-Geek on 2011-01-02 at 00:46
2011-01-02, 01:31   #55
rogue

"Mark"
Apr 2003
Between here and the

23×5×7×23 Posts

Quote:
 Originally Posted by Mini-Geek I haven't quite finished the double check, (still have to do 3893<=j<=4169 on the plus side) but I'm afraid I've found a few primes: Code: p(4169)#*p(2934)-1 p(4169)#*p(3789)-1 p(4169)#*p(2890)+1 p(4169)#*p(3256)+1 All proven prime. There weren't any false factors for these numbers in your posted files, they were listed as candidates, but I do wonder what mistake (human or computer) made you think the multiply side had no primes.

It would have to be a mistake in my double-check script. I just re-ran the script and it found the 2934 PRP (I had it skip the others) and terminated, so I'm confused.

I'm really disappointed. I thought I had this one nailed.

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