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Old 2013-08-16, 17:18   #1
Batalov
 
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Default Top-5000 cutoff is >1 million bits, starting today (now 1.29M))

Sure thing. I emailed C.C. (and added a comment to the prime, too).

I put the asterisk in my morning message, but forgot to post the footnote. It is this:
_______________________
*Note that the Top-5000 cutoff plane will pass exactly 1,000,000 bits today or tomorrow. For the record, right now it is still at 999,400 bits' size, but the 1,290,000-bits abominable primes keep on pouring in. Mark my words Next state of the Top5000 database will be that all primes from position ~1,500 to 5,000 will be ~1,290,000 bits.
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Old 2013-08-17, 04:46   #2
MooMoo2
 
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Quote:
Originally Posted by Batalov View Post
*Note that the Top-5000 cutoff plane will pass exactly 1,000,000 bits today or tomorrow. For the record, right now it is still at 999,400 bits' size, but the 1,290,000-bits abominable primes keep on pouring in. Mark my words Next state of the Top5000 database will be that all primes from position ~1,500 to 5,000 will be ~1,290,000 bits.
Interesting. Here's a quick history of the top 5000 list:
http://tech.groups.yahoo.com/group/p...m/message/8692

Code:
Digits 	Date 		Time to next 10,000
50000 	Jun 22, 2004	13.1 months
60000 	Jul 26, 2005	10.1 months
70000 	May 30, 2006	8.3 months
80000 	Feb 09, 2007	3.1 months
90000 	May 13, 2007	1.5 months
100000 	Jun 29, 2007	6.7 months (average)
150000 	Apr 18, 2010	2.4 months (average)
200000 	Apr 14, 2011	3.2 months (average)
250000 	Aug 09, 2012	2.4 months (average)
300000 	Aug 11, 2013	???

From 50K-100K digits, the average time to increase 10K digits was 7.2 months.
Here's a snapshot of each year:
Code:
Date		Digits of top 5000th prime	Digits to next year
1-1-2001	17261				7477
1-1-2002	24738				5333
1-1-2003	30071				10628
1-1-2004	40699				12908
1-1-2005	53607				10269
1-1-2006	63876				13881
1-1-2007	77757				22597
1-1-2008	100354				4917
1-1-2009	105271				38021
1-1-2010	143292				36415
1-1-2011	179707				26819
1-1-2012	206526				62354
1-1-2013	268880				>32120
1-1-2014	>301000				???
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Old 2013-08-17, 17:20   #3
Kosmaj
 
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Regarding the Top-5000 cut-off or the "water line" it's now right on 1M bits:

Code:
 4998  1089927*2^1000000+1            301037  p197 2006 
 4999  1064099*2^999999+1             301036  g412 2012 
 5000  32883*2^1000004+1              301036   p86 2002 
 5001  2043*2^999925+1                301011 L2998 2012 
 5002  851*2^999854-1                 300989 L1809 2011
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Old 2013-08-17, 17:40   #4
Batalov
 
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...and here's the snapshot of sizes. Observe the plateau at k*2^1290000-1 (388290+a few digits); it will grow longer and then will take over the whole end of the list. As a corollary, after it will happen, the apparent rate of the last Top5000 number's size progression ("to the next 10000") will stop for maybe a year.
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Old 2013-08-17, 21:10   #5
Citrix
 
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Quote:
Originally Posted by Batalov View Post
...and here's the snapshot of sizes. Observe the plateau at k*2^1290000-1 (388290+a few digits); it will grow longer and then will take over the whole end of the list. As a corollary, after it will happen, the apparent rate of the last Top5000 number's size progression ("to the next 10000") will stop for maybe a year.
I think the list would be better, if primes with the same number of digits/bits were given the same rank and primes up to a rank of 5000 were stored on the list.
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Old 2013-08-17, 21:13   #6
firejuggler
 
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but but but... 97 is clearly above 11, even if they both have only 2 digits
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Old 2013-08-17, 21:19   #7
Citrix
 
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Quote:
Originally Posted by firejuggler View Post
but but but... 97 is clearly above 11, even if they both have only 2 digits
maybe they can be
40a
40b

so we have more primes on the list.
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Old 2013-08-18, 02:40   #8
Kosmaj
 
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IMO, that's a good idea! n=1290k will then take less than 10 slots.
But I doubt C.C. will conisider it.

Quote:
Originally Posted by Citrix View Post
I think the list would be better, if primes with the same number of digits/bits were given the same rank and primes up to a rank of 5000 were stored on the list.
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Old 2015-09-12, 19:21   #9
Batalov
 
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Quote:
Originally Posted by Batalov View Post
...and here's the snapshot of sizes. Observe the plateau at k*2^1290000-1 (388290+a few digits); it will grow longer and then will take over the whole end of the list. As a corollary, after it will happen, the apparent rate of the last Top5000 number's size progression ("to the next 10000") will stop for maybe a year.
Today will be the day when the half-twins took over the bottom ~1/e of the Top 5000.
Primes in positions 3188-5000 will now most likely simply squeeze smaller k's replacing with slightly larger, keeping the plateau almost unchanged.
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Old 2015-09-17, 10:06   #10
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Quote:
Originally Posted by Batalov View Post
Today will be the day when the half-twins took over the bottom ~1/e of the Top 5000.
Primes in positions 3188-5000 will now most likely simply squeeze smaller k's replacing with slightly larger, keeping the plateau almost unchanged.
It will pass few weekends more before "your wish come true"

Quote:
To make the top 5000 today a prime must have 388339 digits
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Old 2015-09-17, 15:52   #11
VBCurtis
 
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Quote:
Originally Posted by pepi37 View Post
It will pass few weekends more before "your wish come true"
Huh? What are you talking about? The 5000th prime is from the primegrid effort, as Batalov states.
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