20101224, 19:38  #45 
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. 
20101231, 14:10  #46 
"Mark"
Apr 2003
Between here and the
14450_{8} Posts 
Conjecture disproven?
I believe that I found a k for which no there are no primes, 4169. Could someone please do a doublecheck 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. 
20101231, 15:51  #47 
Apr 2004
11×17 Posts 
double check
I am starting a double check now.
:surprised 
20101231, 16:46  #48 
"Mark"
Apr 2003
Between here and the
2^{3}×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.

20101231, 18:18  #49 
"Mark"
Apr 2003
Between here and the
2^{3}×5×7×23 Posts 
And the ones to test on the divide side.

20101231, 20:17  #50 
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} Last fiddled with by MiniGeek on 20101231 at 20:47 
20101231, 20:46  #51 
"Mark"
Apr 2003
Between here and the
2^{3}·5·7·23 Posts 

20101231, 20:52  #52 
Account Deleted
"Tim Sorbera"
Aug 2006
San Antonio, TX USA
10AD_{16} Posts 
Really? Interesting. Haha. I wasn't sure if it could, especially with it looking like "$ap", so I tried it out, and it looks like it works fine. e.g. here's the start of my pfgw.out:
Code:
p(4169)#*p(1)1 has factors: 687151 p(4169)#/p(1)1 has factors: 2 p(4169)#*p(2)1 is composite: RES64: [753B916ADC6766D6] (12.8772s+5.0848s) p(4169)#/p(2)1 is composite: RES64: [F9C25D55CBB51B98] (12.7213s+4.1486s) Code:
ABC2 p(4169)#$ap($c)$b1 a: in { * / } b: in {  + } c: from 1 to 4169 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) You can also do something like this: Code:
ABC2 349*2^$a0001 a: from 1 to 2 Last fiddled with by MiniGeek on 20101231 at 21:15 
20101231, 21:37  #53 
"Mark"
Apr 2003
Between here and the
2^{3}×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 20101231 at 21:41 
20110102, 00:33  #54 
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 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 MiniGeek on 20110102 at 00:46 
20110102, 01:31  #55  
"Mark"
Apr 2003
Between here and the
2^{3}×5×7×23 Posts 
Quote:
It would have to be a mistake in my doublecheck script. I just reran 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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