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Old 2007-10-11, 19:15   #1
gd_barnes
 
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Default Top-10 twin prime found!

This involves a Riesel prime so is worth posting here. Instead of the little baby twins that I've been searching for, here is a slightly bigger one:

1046619117*2^100000-/+1

It is 9th largest of all time!


Gary
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Old 2007-10-11, 20:11   #2
VBCurtis
 
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Nice find, Gary. I only sieved my ~90k twin candidate up to k=1G... hope I find one before you did.

-curtis
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Old 2007-10-11, 20:37   #3
Cruelty
 
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Congratulations Gary! This is the first "archivable prime" for RPS
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Old 2007-10-11, 21:38   #4
gd_barnes
 
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Default Odds and a couple of offers...

Quote:
Originally Posted by VBCurtis View Post
Nice find, Gary. I only sieved my ~90k twin candidate up to k=1G... hope I find one before you did.

-curtis

Curtis,

As you probably know, technically the odds are in favor of you having to search further. I just got lucky. I calculated that I only had a ~25% chance to find one by k=1.047G for only the odd k's that I sieved. Although it was not as lucky as the original TPS effort on n=195K. As I recall, they stated that they only had a ~22% chance to find one by k=2.004G like they did.

I think it was a slight mistake on my part to sieve only odd k's. There's no reason not to sieve both odd and even k's on twins and then just 'reduce' the form if you find a twin for an even k. I had fully sieved n=100K up to k=4G for odd k's only but that still gave me only a 67% chance of finding a twin, so I could have had to go further. But there's no reason to be searching higher k's then you have to. If I had sieved odd and even k's, I could have had the same chance of finding one by sieving all k<2G.

According to my calculations, if your exponent is exactly n=90K, you have a ~29% chance of finding one by k=1G if you only sieved odd k's. If both odd and even, then a ~49% chance. I based it off of how far I sieved, which was P=130T, but mathematically that doesn't affect the odds of finding one over a specific range of k. It only affects the odds of finding one on each candidate. So it should be pretty accurate.

Tell you what, I'll throw out a couple of offers here:
1. If you want my sieve file for n=100K above n=1.05G that is sieved to P=130T (optimal as far as I could tell), you can have it. Normally, I'd say you could report it yourself since you've shared many sieved files with me, but in this case since it would beat my find , I'd only ask for a share of any twin that you find. But since sieving is such a small part of it, I'd definitely share the next k=2145 prime with you.

2. Since I will now shortly have 2 more cores available that I hadn't expected to have, if you think you'll want more sieving for your n=~90K candidate, I'll be glad to do some sieving for a range above k=1G and send the file your way. Just let me know what range of k and how far you'd like it sieved. Of course you can report all of any twin that you find.


Gary

Last fiddled with by gd_barnes on 2007-10-11 at 21:42
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Old 2007-10-11, 22:19   #5
VBCurtis
 
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Finding a twin is a very low priority for me.. on the machine I am using, it will take the better part of a year to test just the 1G I have so far. The computer I sieved on had but 128mb of memory, which limited me to 1G originally. I've only tested to 15M so far.

If you have new resources suitable for sieving, you should consider doing more with k=5. Sheep is sieving it above 150T, but I eventually have to fill in the work below 150T. I don't mind the work, but there is quite the demand for ranges to test.
-Curtis
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Old 2007-10-11, 23:50   #6
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Congrats on a nice twin!
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Old 2007-10-12, 18:42   #7
gd_barnes
 
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Default sieving on k=5 coming in the near future...

Quote:
Originally Posted by VBCurtis View Post
Finding a twin is a very low priority for me.. on the machine I am using, it will take the better part of a year to test just the 1G I have so far. The computer I sieved on had but 128mb of memory, which limited me to 1G originally. I've only tested to 15M so far.

If you have new resources suitable for sieving, you should consider doing more with k=5. Sheep is sieving it above 150T, but I eventually have to fill in the work below 150T. I don't mind the work, but there is quite the demand for ranges to test.
-Curtis
Thanks, Kosmaj!

Curtis,

OK, sieving resources coming your way on k=5 in the near future. Give me about a week or so. The machines that just finished up the TPS are P4's, which as you know are poor at sieving and I'll throw them at my other LLRing efforts. I'd use them for sieving a lower priority effort like going higher on your TPS but not for a high-priority effort like k=5. I have 2 cores on my one new dual-core Athlon laptop that I use almost exclusively for sieving because it's slower at LLRing. I have another project that's been sieving for about 2 weeks with about 1 week to go and I want to finish it up first.


Gary

Last fiddled with by gd_barnes on 2007-10-12 at 18:47
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