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-   -   Top-5000 cutoff is >1 million bits, starting today (now 1.29M)) (https://www.mersenneforum.org/showthread.php?t=18482)

Batalov 2013-08-16 17:18

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 [URL="http://primes.utm.edu/primes/page.php?rank=5000"]cutoff plane[/URL] 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 :paul: Next state of the Top5000 database will be that [B][I]all[/I][/B] primes from position ~1,500 to 5,000 will be ~1,290,000 bits.

MooMoo2 2013-08-17 04:46

[QUOTE=Batalov;349814]
*Note that the Top-5000 [URL="http://primes.utm.edu/primes/page.php?rank=5000"]cutoff plane[/URL] 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 :paul: Next state of the Top5000 database will be that [B][I]all[/I][/B] primes from position ~1,500 to 5,000 will be ~1,290,000 bits.[/QUOTE]
Interesting. Here's a quick history of the top 5000 list:
[url]http://tech.groups.yahoo.com/group/primeform/message/8692[/url]

[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.
[/code]

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 ???
[/code]

Kosmaj 2013-08-17 17:20

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
[B] 5000 32883*2^1000004+1 301036 p86 2002 [/B]
5001 2043*2^999925+1 301011 L2998 2012
5002 851*2^999854-1 300989 L1809 2011
[/CODE]

Batalov 2013-08-17 17:40

1 Attachment(s)
...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.

Citrix 2013-08-17 21:10

[QUOTE=Batalov;349947]...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.[/QUOTE]

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.

firejuggler 2013-08-17 21:13

but but but... 97 is clearly above 11, even if they both have only 2 digits

Citrix 2013-08-17 21:19

[QUOTE=firejuggler;349970]but but but... 97 is clearly above 11, even if they both have only 2 digits[/QUOTE]

maybe they can be
40a
40b

so we have more primes on the list.

Kosmaj 2013-08-18 02:40

IMO, that's a good idea! n=1290k will then take less than 10 slots.
But I doubt C.C. will conisider it.

[QUOTE=Citrix;349969]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.[/QUOTE]

Batalov 2015-09-12 19:21

[QUOTE=Batalov;349947]...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.[/QUOTE]
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.

pepi37 2015-09-17 10:06

[QUOTE=Batalov;410162]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.[/QUOTE]
It will pass few weekends more before "your wish come true" :smile:

[QUOTE]To make the top 5000 [I]today[/I] a prime must have 388339 digits[/QUOTE]

VBCurtis 2015-09-17 15:52

[QUOTE=pepi37;410604]It will pass few weekends more before "your wish come true" :smile:[/QUOTE]

Huh? What are you talking about? The 5000th prime is from the primegrid effort, as Batalov states.


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