Report top-5000 primes for k=1003-3000
 

Please report all top-5000 primes for k=1003-3000 in this thread.

Kar_bon has a list of all primes found and search-ranges previously completed on the k's that we will be searching [URL="http://www.rieselprime.de/Data/00300.htm"]here for k=1003-2000[/URL] and [URL="http://www.rieselprime.de/Data/02000.htm"]here for k=2000-3000[/URL]. It includes all known n-ranges starting at n=1 and will be updated as we complete ranges and find primes.

Instructions for submitting a top-5000 prime:

Go to [URL="http://primes.utm.edu/primes/home.php"][COLOR=#810081]http://primes.utm.edu/primes/home.php[/COLOR][/URL].

Step 1: For people who have not submitted top-5000 primes previously, create a prover account:
1. Select 'Submit' on the lower left side under 'Join in'.
2. Select the 'click here to create a prover-account' link in the middle of the page.
3. Fill out the form and submit it. You will be assigned a prover account.

Step 2: Create a proof code:
1. Go to the home page in the link above and select 'Index' on the left side under 'Provers'.
2. Next to 'search prover-accounts', type yours and press enter.
3. Click on your prover account (there may be one or several) and press enter.
4. Towards the bottom, click on 'Create a New Proof-Code' and press enter.
5. If necessary in the little pop-up box, type in your user name (prover account) and password and press enter.
6. You should now have a list of proof programs. Select LLR.
7. In the space below all the programs that says "none", type "NPLB, srsieve, psieve" (WITH the comma but without quotes) for the project and sieving software. (Obviously if you did an individual-k search on your own, then the software may vary.)
8. You should now have a new proof code and can submit the prime. Example...L442.

Step 3: Submit the prime:
1. Go to the home page in the link above and select 'Index' on the left side under 'Provers'.
2. Next to 'search proof-code', type your new code from step 2 and press enter.
3. Towards the bottom, next to 'Submit primes using this code as', click on your name (prover account) and press enter.
4. If necessary in the little pop-up box, type in your user name (prover account) and password and press enter.
5. You should see a big free-form box. Type in your prime (no spaces needed) and click 'Press here to submit these prime(s)'.
6. A verification screen will come up. If the prime is correct, click 'Press here to complete submission'.


Gary

1371*2^351106-1 is confirmed prime

user=nuggetprime
[2009-01-02 02:32:56]
1647*2^351262-1 is prime! Time : 146.0 sec.

[URL]http://primes.utm.edu/primes/page.php?id=79093[/URL]
[FONT=Verdana]user=henryzz[/FONT]
[FONT=Verdana][2009-01-02 08:35:30][/FONT]
[FONT=Verdana]1127*2^351674-1 is prime! Time : 615.0 sec.[/FONT]
[FONT=Verdana]confirmed prime:cry:
[/FONT]

[FONT=Verdana]user=IronBits[/FONT]
[FONT=Verdana][2009-01-02 10:54:31][/FONT]
[FONT=Verdana]1457*2^351812-1 is prime! Time : 174.0 sec.

[/FONT][COLOR=green]The following warnings have been noted:[/COLOR]

[LIST][COLOR=green][*]At the rate at which primes have been added to this list in the past,[*]the 105910 digit prime "1457*2^351812-1" may only be on the list for about 2 weeks.[/COLOR][/LIST]Already in database [URL="http://primes.utm.edu/primes/page.php?id=85983"]85983[/URL] : 1457*2^351812-1 :cry:

[FONT=Verdana]user=em99010pepe[/FONT]
[FONT=Verdana][2009-01-02 11:38:10][/FONT]
[FONT=Verdana]1195*2^351457-1 is prime! Time : 22864.0 sec.

(confirmed one)
[/FONT]

1491*2^351886-1 is confirmed prime

I have deleted some smaller primes and some posts related to the inadvertant restart of the 8th drive from this thread, changed it's title slightly, and edited the 1st post to make it for n>200K primes only.


Gary

1539*2^352111-1 is a confirmed prime

1943*2^352182-1 is prime

Note: This in only 271 digits higher than #5000. We are just barely ahead of the wave, 4962 place

I suppose it's appropriate that this is a confirmed prime since I found it in my first 200-300 tests of port 8000:

1567*2^352397-1 is confirmed prime

It looks like Chris has a new one though. That's 2 new and 2 confirmed primes in ~12 hours. Now this is what I would call fun! :-)

Yep. :smile:
[FONT=Verdana]1673*2^352222-1 is prime.
Nobody make any sudden movements or it will fall off the list.
[/FONT]

1923*2^352462-1 is prime

Are we having fun yet? :smile:

I like the top-5000 score of these primes. This is the first one of the 3 in the new drive that scored > 1.01. lmao

1643*2^352606-1 is prime

1699*2^352587-1 is confirmed prime

A remarkable pair only n=58 apart for k=1643:

1643*2^352664-1 is prime


352K-353K is a highly prolific range. After 350K-351K had no primes even for the larger k=1005-2000 range, we've already 8 primes for 352K-353K (including prior known) for k=1400-2000 and there's still quite a bit to go.

1669*2^353119-1 is prime

1557*2^353309-1 is confirmed prime

1483*2^355039-1 is a confirmed prime

1575*2^355060-1 is prime! Time : 188.0 sec.
confirmed

(Edit by Max: moved here from the 8th Drive thread)

1485*2^355643-1 is confirmed prime


Where'd all the NEW primes go?

1737*2^355712-1 is confirmed prime

1663*2^356015-1 is prime

[QUOTE=gd_barnes;159336]Where'd all the NEW primes go?[/QUOTE]

Hundreds of them:
[url]http://stats.ironbits.net/statsnew/prime_list.php?a=reset[/url]
updated every hour - it will drive the mailer

1577*2^356616-1 is prime!
confirmed

1671*2^357110-1 is prime.

[quote=AMDave;159368]Hundreds of them:
[URL]http://stats.ironbits.net/statsnew/prime_list.php?a=reset[/URL]
updated every hour - it will drive the mailer[/quote]


I meant new, as in reportable top-5000 primes, on the 8th drive.

I assume that the mailer knows not to send Emails on port 9000.


Thanks,
Gary

1517*2^356384-1 is confirmed prime
1617*2^356462-1 is prime
1487*2^356506-1 is confirmed prime
1623*2^356936-1 is prime

:smile:


Very odd: Where'd all the k=1700-2000 primes go on the 8th drive? On the entire drive, we've had a total of 2 new primes and 1 confirmed prime for that range. For k=1400-1700, we've had multitudes of them.


Gary

1403*2^359146-1 is confirmed prime
1609*2^359209-1 is prime


I think k=1700-2000 is a nearly barren range! For n=350K to the current processing limit, we have:

23 total primes for k=1400-1700

3 total primes for k=1700-2000

This includes confirmed primes so is not biased by previous searching in any way.

As Chris is fond of me saying: Primes are very strange! :smile:


Gary

[quote=gd_barnes;159578]1403*2^359146-1 is confirmed prime
1609*2^359209-1 is prime


I think k=1700-2000 is a nearly barren range! For n=350K to the current processing limit, we have:

23 total primes for k=1400-1700

3 total primes for k=1700-2000

This includes confirmed primes so is not biased by previous searching in any way.

As Chris is fond of me saying: Primes are very strange! :smile:


Gary[/quote]
There's [I]very strange[/I] and then there's [I]really weird[/I].
This sort of thing used to drive me nuts when I would do (semi)fixed n tests. Five primes for one n, then none for the next etc.

1785*2^359725-1 is confirmed prime

We've completed n=350K-360K minus some stragglers. The unofficial final count is:

k=1400-1700 23 primes
k=1700-2000 4 primes

1625*2^361306-1 is prime


This is getting stranger by the minute: Now, in addition to the previous ridiculous ratio of k=1400-1700 vs. 1700-2000 primes, we have an unbelievable 9 CONSECUTIVE NEW primes for k=1600-1700!!

Although this is a little biased towards the k=1600-1700 and 1800-2000 ranges that have had little searching done on them...9 consecutive in a k=100 range? Come on, what's going on here? Where are the k=1800-2000 primes as well as others from many k's that haven't been searched for k=1400-1600 & 1700-1800?

Counting all primes to remove any bias from ones previously found, since n=350K, we now have:
[code]
k-value # primes
1400-1500 6
1500-1600 6
1600-1700 12
1700-1800 2
1800-1900 0
1900-2000 2
[/code]

[There is a k=1800-1900 already-known prime in Ian's reserved manual range so finally the barren stretch there will be broken.]

Not only are primes strange, they can be downright bizarre!

It's things like this that lead one to conclude that primes are not random and is a large part of the reason that we search huge ranges of k and n all at once...to ultimately help decipher the "code" of primes. :smile:


Gary

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=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

[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

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

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

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

[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

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

[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:

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

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

1955*2^364156-1 is prime

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

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

1483*2^365027-1 is confirmed prime

[FONT=Verdana]1667*2^365342-1 is prime
[/FONT]

1655*2^365228-1 is prime

1601*2^365302-1 is prime

1 out of the last 17 primes hasnt been 1600-1700
amazing:surprised

1587*2^365549-1
1603*2^364139-1
Confirmed primes.

[FONT=Verdana]1683*2^366866-1 is prime.
[/FONT]

1941*2^365467-1 is prime
1637*2^368470-1 is prime

Brucifer found:

1635*2^366428-1 is confirmed prime

LaurenU2 found:

1463*2^368756-1 is confirmed prime
1561*2^369477-1 is confirmed prime

[quote=henryzz;159863]1 out of the last 17 primes hasnt been 1600-1700
amazing:surprised[/quote]

Make that 1 out of the last 17 NEW primes hasn't been k=1600-1700.

Now it's: 18 out of the last 20 NEW primes HAS been k=1600-1700 and the other 2 have been k=1900-2000.

(I don't like negative logic. lol) :smile:

Somewhere in there are some k=1400-1600 & k=1700-1900 new primes I'm sure. Those areas are far from having been fully searched already, especially the k=1700-1900 range. We're slowly getting a higher percentage of new primes as we get higher. Above n=375K, the previously known primes drops dramatically. That's why I'm very excited by the prospects for the rally!


Gary

The streak of k=1600-1700 & 1900-2000 new primes will finally end and with a vengence!...

Flatlander, Laurenu2, and PCZ all have new primes! :smile:

1727*2^370942-1 is a confirmed prime

[FONT=Verdana]user=em99010pepe[/FONT]
[FONT=Verdana][2009-01-23 00:24:42][/FONT]
[FONT=Verdana]1527*2^366989-1 is prime! Time : 31033.0 sec. (confirmed)[/FONT]


[FONT=Verdana]user=PCZ[/FONT]
[FONT=Verdana][2009-01-23 00:53:05][/FONT]
[FONT=Verdana]1953*2^370639-1 is prime! Time : 1469.0 sec. (new)[/FONT]

user=Free-DC Mercenaries
[2009-01-23 04:54:28]
1555*2^372227-1 is prime! Time : 4965.0 sec. (confirmed)

Our first new k=1800-1900 prime of this drive:

1865*2^372352-1 is prime

There was a new one found first several hours ago but it hasn't been reported yet.

[FONT=Verdana]1505*2^370016-1 is prime.
[/FONT]

1459*2^373251-1
in database already :(

[quote=Flatlander;160019][FONT=Verdana]1505*2^370016-1 is prime.
[/FONT][/quote]

Our first new k=1500-1600 prime of the drive. This is the prime that officially ended the streak of 24 consecutive new k=1600-1700 & 1900-2000 primes! :smile:

1999*2^376443-1
Was added to the primes database ...

1631*2^375114-1

1583*2^374660-1 is confirmed prime

1887*2^379364-1 is prime

1507*2^380353-1 is a confirmed prime

Primes not previously listed in this thread:

New primes found & submitted at top-5000:

Found by Beyond:
1849*2^374015-1
1969*2^375669-1

Confirmed primes found:

Found by LaurenU2:
1525*2^372061-1
1815*2^376878-1
1757*2^383700-1

Found by Beyond:
1595*2^374112-1
1569*2^374255-1
1493*2^377656-1


2 new primes have been found by LaurenU2; one over a day old. Specifics have now been sent in an Email.

2 more new primes were found by Free-DC-Mercenaries and 1 more by AMDave in the last 3 hours. No follow-up needed. I'm sure they will submit them within the next several hours.


Gary

1715*2^384264-1 is confirmed prime

[FONT=Verdana]Free-DC Mercenaries[/FONT]
[FONT=Verdana][2009-01-23 21:06:05][/FONT]
[FONT=Verdana]1817*2^381708-1 is prime! Time : 2840.0 sec.[/FONT]


[FONT=Verdana]Free-DC Mercenaries[/FONT]
[FONT=Verdana][2009-01-23 18:26:09][/FONT]
[FONT=Verdana]1957*2^380189-1 is prime! Time : 2804.0 sec.[/FONT]

[FONT=Verdana]Free-DC Mercenaries[/FONT]
[FONT=Verdana][2009-01-24 03:39:10][/FONT]
[FONT=Verdana]1547*2^385550-1 is prime! Time : 2914.0 sec. (confirmed)[/FONT]

1855*2^384059-1 is prime

1779*2^384925-1 is a confirmed prime

[FONT=Verdana]Free-DC Mercenaries[/FONT]
[FONT=Verdana][2009-01-24 08:47:06][/FONT]
[FONT=Verdana]1491*2^388903-1 is prime! Time : 2939.0 sec.[/FONT]

user=Free-DC Mercenaries
[2009-01-24 10:13:31]
1959*2^389797-1 is prime! Time : 2869.0 sec.

1821*2^389237-1

1887*2^390993-1

1665*2^391531-1 is confirmed prime

1749*2^391615-1
already in the database

1515*2^391554-1 is a confirmed prime not listed on the "known primes list"

Neither was 1665*2^391531-1, 1749*2^391615-1 or 1741*2^392029-1

1467*2^393086-1 is prime

My first new primes of the rally: :smile:

1979*2^392404-1 is prime
1629*2^392428-1 is prime


Keep up the great work everyone! :flex:

[quote=MyDogBuster;160262]1515*2^391554-1 is a confirmed prime not listed on the "known primes list"

Neither was 1665*2^391531-1, 1749*2^391615-1 or 1741*2^392029-1[/quote]

In addition to those 4, also missing was: 1935*2^390087-1, 1731*2^390343-1, 1427*2^391542-1, & 1761*2^393653-1. Ugh!

Thanks for letting me know. Sorry about that.

It appears there was a "hole" in the list of previously known primes for n=389K-393.7K and 8 of them were missing. I've now double-checked the entire list and can guarantee that it is now correct up to n=420K. There are still some areas that look like holes but they are correct this time.

In a little while, I'll update the new and confirmed primes found with the rally. In the mean time, I'm going to set up a new account and proof code for Lauren. After that, he'll have several new primes that he can submit. :-)

Trying to select only the k=1400-2000 primes off of top-5000 is not easy. I either messed up my selection criteria or forgot to tell it to list more than 20 primes on a page, which I've caught myself doing before. The latter would explain the "hole" in previously known primes.


Gary

1761*2^393653-1 is confirmed prime (Not Listed either)

1797*2^393797-1 is confirmed prime

1875*2^392871-1
Added to the database

1473*2^381363-1 is prime! & added.

1577*2^373062-1 is confirmed prime

(apologies guys, I have been busy, but I am catching up :) )

1629*2^397213-1 is prime

[FONT=&quot]1749*2^397157-1
already in the database
[/FONT]

Per Bok's instructions for me to input his primes as me...

Already in database [URL="http://primes.utm.edu/primes/page.php?id=86293"]86293[/URL] : 1501*2^386595-1
Added [URL="http://primes.utm.edu/primes/page.php?id=86384"]86384[/URL] : 1875*2^394864-1 (118870 digits)

1489*2^398757-1 is prime

1503*2^397527-1 is confirmed prime

1729*2^400007-1 is a confirmed prime

Already in database [URL="http://primes.utm.edu/primes/page.php?id=78493"]78493[/URL] : 1905*2^399686-1

[FONT=Verdana]henryzz[/FONT]
[FONT=Verdana][2009-01-24 11:45:03][/FONT]
[FONT=Verdana]1803*2^391127-1 is prime! Time : 807.0 sec.[/FONT]

After conferring with LaurenU2 by Email, I have created a new top-5000 prover account and proof code for him and submitted the following new primes for him:

1853*2^370128-1
1887*2^377976-1
1449*2^386620-1
1445*2^388290-1
1447*2^400365-1


Gary

[FONT=Calibri]1591*2^399861-1 Is a confirmed prime[/FONT]
[FONT=Calibri][/FONT]
[FONT=Calibri]/Lennart[/FONT]

Previously found and submitted primes not shown in this thread:

New primes submitted at top-5000,
all found by Beyond:

1831*2^385475-1
1821*2^385633-1
1953*2^388967-1
1955*2^391522-1
1561*2^392253-1
1487*2^392568-1
1625*2^397258-1
1863*2^397915-1
1479*2^398223-1

Confirmed primes:

Found by LaurenU2:
1471*2^386575-1
1655*2^400052-1

Found by Beyond:
1475*2^388108-1
1431*2^389415-1
1935*2^390087-1
1731*2^390343-1
1427*2^391542-1
1741*2^392029-1

Found by MrOzzy:
1431*2^396111-1


All as of Jan. 25th at 4:00 AM Arizona time (11 AM GMT).


Gary

As of Jan. 25th at 4:00 AM Arizona time (11 AM GMT), the following folks have new top-5000 primes to submit:

MrOzzy 1
Beyond 1
Petey 2


I'll send PM's to MrOzzy and Beyond with their primes. I'll send an Email to Petey seeing if he would like help in submitting his primes.


Gary

It has been months since I've found a prime. So far I was the most unlucky person of NPLB, I don't know if I still am but, I got to do the math again.

Anway: 1985*2^388208-1 is prime!

[quote=MrOzzy;160357]It has been months since I've found a prime. So far I was the most unlucky person of NPLB, I don't know if I still am but, I got to do the math again.

Anway: 1985*2^388208-1 is prime![/quote]

I guess I still am the worst off, I just did the math:

number of primes vs tested pairs:

Petey 1381
PCZ 1536
henryzz 1556
AMDave 1803
em99010pepe 1931
alpha 2061
IronBits 2194
Free-DCMercenaries 2366
Flatlander 2593
BlisteringSheep 2728
glennpat 3060
gd_barnes 3582
Beyond 3791
Mini-Geek 4067
mdettweiler 4560
AES 5109
MyDogBuster 5618
KAMCOBILL 5953
Bok 6293
DragonOrta 6349
kar_bon 6353
Helix-Von-Smelix 6362
tnerual 6787
Laurenu2 7034
nuggetprime 7402
sm5ymt 7869
Jokern3000 8349
Kman1293 8355
Brucifer 10700
MrOzzy 10871

My simpathy is with Brucifer here :-)

Prime score vs pair score:

Free-DCMercenaries 2446
Mini-Geek 2596
Petey 2674
Beyond 4227
henryzz 4321
Kman1293 5148
AMDave 5154
glennpat 5301
KAMCOBILL 5306
AES 5657
IronBits 5769
Jokern3000 5793
tnerual 5893
MyDogBuster 5943
PCZ 5962
gd_barnes 6125
mdettweiler 6437
Bok 6502
sm5ymt 6647
kar_bon 6720
Helix-Von-Smelix 6977
BlisteringSheep 7376
alpha 7427
Laurenu2 7465
Flatlander 7717
Brucifer 10766
em99010pepe 10843
MrOzzy 17190

I only have simpathy with myself here :D

Maybe this can be included in the stats, so I can pity myself every day?

Already in database [URL="http://primes.utm.edu/primes/page.php?id=85765"]85765[/URL] : 1587*2^402941-1
Already in database [URL="http://primes.utm.edu/primes/page.php?id=85478"]85478[/URL] : 1431*2^405961-1