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-   -   Report top-5000 primes for k=1003-3000 (https://www.mersenneforum.org/showthread.php?t=11246)

gd_barnes 2009-01-21 14:26

[quote=Mini-Geek;159706]What's the average weight (or combined weight or something) of the k's in 1600-1700 vs the other k=100 ranges? Also, I'd bet that if somebody worked the math out, this is bound to happen some time or another, just like GIMPS's two primes two weeks apart, which seems impossibly unlikely, but it worked out to be a decent probability over as much time as GIMPS has been around and assuming 1 prime/year (which they shouldn't 'expect', by prime heuristics, but they seem to be in a dense area of Mersennes).[/quote]


I'm not sure of the avg. weight but it'd be a relatively quick excercise to do it by looking at Rieselprime.org. For 50 k's in each 100k range, I doubt the average is much different than any other 100k range. Even if it was, it wouldn't explain such a deviation. If you want and have time, feel free to post your findings here.

You think exactly like I do. I know what are random events seem like non-random because there are so many multidues of possibilities for those events. People frequently associate such random events with miracles, mystic happenings, etc., which is completely bogus.

This is likely just one of those "random" fluctuations from the mean as though you got 75-80 heads when flipping a random coin 100 times. If you did 1 million tests of 100 coin flips, you'll most likely get 75-80 heads at some point. It'd be easy enough to do the math to figure the odds of this happening but I don't have time right now. For all I know, it could take 1 billion such tests on average.

In the prime number world though, I don't think we have clear proof yet that these things are completely random yet so when apparently non-random "clumpings" occur, it makes even the most logical amongst us wonder a little bit.

From my 21-month experience in prime searching, I believe this is the most unusual clumping that I have seen. But since I've had 21 months to witness such a thing, it's probably random. (lol)

Edit: I just noticed that Chris found a new prime on port 8000 and guess what: It's k=1600-1700...that's TEN consecutive new primes in that range. Now I can say that primes are very VERY strange.


Gary

Flatlander 2009-01-21 14:39

[quote=gd_barnes;159711]...
Edit: I just noticed that Chris found a new prime on port 8000 and guess what: It's k=1600-1700...that's TEN consecutive new primes in that range. Now I can say that primes are very VERY strange.

Gary[/quote]

1697*2^361566-1
1629*2^362181-1
are prime! :smile:
Try to keep up Gary! lol

gd_barnes 2009-01-21 14:46

Funny Chris: I just saw your 2nd new prime come up with my confirmed one:

1475*2^362176-1 is confirmed prime

With Chris's two finds here, we can now make that 11 consecutive new primes found for k=1600-1700. This has become so outlandishly bizzare that I went and checked the k/n pairs that are being handed out in David's server: Plenty of k=1800-2000 candidates in there. With little searching having been previously done in that area, I'm dumbfounded. The count now stands:

[code]
k-value # primes
1400-1500 7
1500-1600 6
1600-1700 14
1700-1800 2
1800-1900 0
1900-2000 2
[/code]


It's now 27-4 in favor of k=1400-1700.


Gary

Flatlander 2009-01-21 17:43

I just received a second email for [FONT=Verdana]1697*2^361566-1

I tried to enter it in top-5000!
[/FONT]

gd_barnes 2009-01-21 17:55

[quote=Flatlander;159731]I just received a second email for [FONT=Verdana]1697*2^361566-1[/FONT]

[FONT=Verdana]I tried to enter it in top-5000![/FONT]
[/quote]


What? The prime that you just submitted a couple of hours ago doesn't look familiar to you? lol

In the mean time, can anyone say 12 in a row new primes for k=1600-1700?:

1689*2^362388-1 is prime



If this continues for another couple of primes, I'm going to do some serious investigation on # of k/n pairs/avg. weight/what k's have already been searched/etc. I may have been in prime-searching for only 21 months, but this is not something that should happen once in 21 months...more like once in 21 years!

I'm quite confident that k=1800-1900 & 1900-2000 have been searched no more than k=1600-1700 so if you allow the 1st prime in the streak to be any one of the 3, then the chances on any 12-prime sequence coming up 12 in a row in one of the 3 are 1 in 3^11 = 177147.

What that means is that I would have had to have witnessed or been involved in the searching of 177147 top-5000 primes by now. In 21 years, sure, but not 21 months. In non-top-5000 primes, sure, but not top-5000 primes.

Go figure!

Gary

Flatlander 2009-01-21 18:00

Can I reserve k=1600-1700, n = 365,000-400,000? :grin:

IronBits 2009-01-21 20:28

[quote=Flatlander;159731]I just received a second email for [FONT=Verdana]1697*2^361566-1

I tried to enter it in top-5000!
[/FONT][/quote]
My BAD. I didn't see it in my Sent Items, so wanted to make sure you got a notice.
When AMDave gets the auto-notify working from the database, you all will receive duplicate notices until we are sure it's solid, then I'll stop my vbscript auto-notify routine, and yet another windows script goes bye-bye :smile:

gd_barnes 2009-01-22 04:03

How about 13 in a row?:

1661*2^362878-1 is prime

Also:
1783*2^362647-1 is confirmed prime
1557*2^362769-1 is confirmed prime

gd_barnes 2009-01-22 09:26

The k=1600-1700 new prime streak finally ends at 13:

1955*2^364156-1 is prime

gd_barnes 2009-01-22 11:42

1493*2^364348-1 is confirmed prime
1587*2^364520-1 is confirmed prime

gd_barnes 2009-01-22 15:21

I'll gladly slay this high-prior-known prime area before we start the rally:

1483*2^365027-1 is confirmed prime


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