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Old 2010-12-24, 19:38   #45
Harvey563
 
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Default 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.


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Old 2010-12-31, 14:10   #46
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Default 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.
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Old 2010-12-31, 15:51   #47
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Default double check

I am starting a double check now.


:surprised
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Old 2010-12-31, 16:46   #48
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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
File Type: zip mul_4169.zip (40.9 KB, 234 views)
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Old 2010-12-31, 18:18   #49
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And the ones to test on the divide side.
Attached Files
File Type: zip div_4169.zip (40.9 KB, 239 views)
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Old 2010-12-31, 20:17   #50
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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
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Old 2010-12-31, 20:46   #51
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Quote:
Originally Posted by Mini-Geek View Post
I am also running a double check, using an unsieved ABC2 file (below) and -f.
Code:
ABC2 p(4169)#$ap($b)$c
a: in { * / }
b: from 1 to 4169
c: in { -1 +1}
Interesting. I didn't realize that PFGW could substitute symbols.
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Old 2010-12-31, 20:52   #52
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Quote:
Originally Posted by rogue View Post
Interesting. I didn't realize that PFGW could substitute symbols.
Really? Interesting. Haha. I wasn't sure if it could, especially with it looking like "$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
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Old 2010-12-31, 21:37   #53
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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
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Old 2011-01-02, 00:33   #54
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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
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Old 2011-01-02, 01:31   #55
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Quote:
Originally Posted by Mini-Geek View Post
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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