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Old 2022-08-15, 22:54   #584
mathwiz
 
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Quote:
Originally Posted by Viliam Furik View Post
I propose the name "Great Wave of TuckerKao" - to be pronounced "Tuck-er-cow-uh" (a play on the name of the woodprint - Great Wave off Kanagawa) from the collection of "168 ranges of Mount Bullshit" (a play on the name of the collection - 36 views of Mount Fuji).

What do you think, forumites?
I think you're spending way more mental energy on the kid than any of this nonsense deserves...
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Old 2022-08-16, 10:51   #585
Viliam Furik
 
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Originally Posted by mathwiz View Post
I think you're spending way more mental energy on the kid than any of this nonsense deserves...
Yes, but the humor that comes out of it is really good. I think it's worth it. "Great Wave of TuckerKao", that's just golden.

Last fiddled with by Viliam Furik on 2022-08-16 at 10:52
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Old 2022-08-19, 18:58   #586
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Scored a 5 pointer today. Found 5 new factors all from the M168.6M subrange: M168682169, M168682681, M168687641, M168697079, M168697693.

Quote:
Originally Posted by Viliam Furik View Post
Yes, but the humor that comes out of it is really good. I think it's worth it. "Great Wave of TuckerKao", that's just golden.
The greatness of the wave have often been the quantity or the worth of the total exponents involved. If Zhangrc could have finished the trial factoring of all the M108.3M candidates from 276 and 277 all by himself within 3~4 months, that would have been golden also.

Owning a full set of Monopoly deeds will worth way more than the sum of the individual cards.
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Old 2022-08-19, 19:41   #587
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Originally Posted by tuckerkao View Post
Scored a 5 pointer today. Found 5 new factors all from the M168.6M subrange: M168682169, M168682681, M168687641, M168697079, M168697693.
You celebrate finding factors in that range. That is odd. Wouldn't you want fewer factors in that range? Each factor found proves that number could not possibly be a Mersenne Prime. That means the overall chance of any number in that range to be found to be prime goes down. (Because we know that each PRP/LL test has a certain chance of finding a prime. And with fewer numbers to test, your multiple against that ratio goes down.)
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Old 2022-08-19, 20:28   #588
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Originally Posted by Uncwilly View Post
(Because we know that each PRP/LL test has a certain chance of finding a prime. And with fewer numbers to test, your multiple against that ratio goes down.)
I'd rather prove the exponents to be composite using TFs than PRPs if possible such as M168104323 and M168113423 which the factors were found from the bit levels outside the GPU72 recommendations, I've placed my predictions on M168,***,*23 not all the M168M exponents. The quicker all the PRP tests to be finished, the sooner I'll know the final result. Too many PRP tests = other users won't even want to run the PRP tests for them.

With the most recent 5 factors found, I'll probably avoid PRP tests between M168,680,000 to M168,700,000 for now.

Consider this imaginary scenario: if I were already finished 92% of the PRP tests of all the M168,***,*23 exponents with only 20+ candidates left, ATH and Kriesel will probably be willing to just join the force and finish them ahead of me.

When all the M168M exponents are trial factored deeper, I kind of want to go after M168.6M especially M168641923, because it's still sort of more factor-resistant subrange than M168.4M as of the records today.

If I don't find any factors with 2,000+ attempts, that means my GPU is out of order, why would I celebrate for that?

This is the real progress of the PRP tests done from the M168,***,*23 candidates so far - https://www.mersenne.org/report_prp/...dispdate=1&B1=


For me:

The Winning Scenario: 1 M168.***.*23 turns out to be Mersenne Prime.

The Losing Scenario: All M168.***.*23 turns out to be proven composites or Someone else found a Mersenne Prime greater than M82589933 but lesser than M168,000,000.

Last fiddled with by tuckerkao on 2022-08-19 at 21:07
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Old 2022-08-19, 23:54   #589
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Quote:
Originally Posted by tuckerkao View Post
The Winning Scenario: 1 M168.***.*23 turns out to be Mersenne Prime.

The Losing Scenario: All M168.***.*23 turns out to be proven composites or Someone else found a Mersenne Prime greater than M82589933 but lesser than M168,000,000.
You do understand that every time you find a factor in your silly magic range, you're closer to "The Losing Scenario", right?
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Old 2022-08-20, 00:41   #590
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You do understand that every time you find a factor in your silly magic range, you're closer to "The Losing Scenario", right?
I don't understand the probabilities of this. Whenever someone brings the trial factoring bits up higher for an entire subrange, more exponents will for sure be factored, but it doesn't change the total amount of PRP tests needed in the future. Those exponents with the lower TF bits or without P-1 will still get the prior works completed before the PRP tests.

Using M111.2M vs M168.6M as the example, M168.6M has the higher chance to yield a Mersenne Prime because the total amount of unfactored exponents is much higher: 2,047 vs 1,788. There will be no way that M168.6M will only have 1,788 unfactored exponents outstanding after all exponents been trial factored up to 277 or 278. Maybe check M168.4M which already had more TF works done.

Last fiddled with by tuckerkao on 2022-08-20 at 01:14
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Old 2022-08-20, 06:21   #591
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Originally Posted by tuckerkao View Post
I don't understand the probabilities of this. Whenever someone brings the trial factoring bits up higher for an entire subrange, more exponents will for sure be factored, but it doesn't change the total amount of PRP tests needed in the future. .
Take this to its logical conclusion- if you found factors for every candidate in the entire range, how many prp tests would there be left to run?
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Old 2022-08-22, 16:01   #592
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Originally Posted by VBCurtis View Post
Take this to its logical conclusion- if you found factors for every candidate in the entire range, how many prp tests would there be left to run?
Definitely zero and it means there is no Mersenne Prime there.

Finding a new factor after every additional 70~85 trial factoring attempts in average should be part of the familiar equation which won't decrease the chance of finding a new Mersenne Prime because if a top user like SRBase or TheJudger goes quickly through any lower subranges such as M125.7M and brings it up to 278, certain amount of exponent candidates will expectedly be eliminated.

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I find this to be a useful contribution.

I don't see any reason to discourage people to test whatever exponents that want. Just because some people are hyper-focussed on the leading edge stuff doesn't make it the only thing we should care about. Nor does it mean any other testing not currently advancing their goals is worth anything less.

Go for it tuckerkao, keep testing your exponents. Good luck.
I don't see anything wrong with running PRPs in the M168M range, it takes around 9-10 days per exponent not including the PC rest time. Something definitely doable and doesn't stick too long. If a PRP takes much longer than a full month, then it's probably too large with the possibilities that the final result may not be reliable.

I just checked that the average TF bits of the entire M168M is around 75.4 which is much higher than the neighboring ranges that have been generally covered by SRBase(Average TFs = 74.1 or 74.2).

Last fiddled with by tuckerkao on 2022-08-22 at 17:01
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Old 2022-08-23, 07:51   #593
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Quote:
Originally Posted by tuckerkao View Post
I don't see anything wrong with running PRPs in the M168M range
Wrong? No, it is perfect!
Wrong is when you ask other people to run them for you.
If you run them by yourself, is excellent!

Last fiddled with by LaurV on 2022-08-23 at 07:51 Reason: spacing
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Old 2022-09-01, 23:38   #594
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I scored a 6-pointer today, renewed my previous best record: M168605477, M168605573, M168607259, M168607529, M168608093, M168608257.

Quote:
Originally Posted by mathwiz View Post
You do understand that every time you find a factor in your silly magic range, you're closer to "The Losing Scenario", right?
I had played several monopoly games which I was only 1 to 2 steps away from bankruptcy, then managed a comeback and won. There were also occasions which I was ahead of the game almost all the way, then suddenly lose. The chance will usually be hard to call too early. Unless a checkmate call has been announced(someone lands a new P-PRP result), otherwise it'd be considered too early to decide.

Last fiddled with by tuckerkao on 2022-09-01 at 23:46
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