[QUOTE=unconnected;375706]Can't wait another day to complete N+1 test. So I submit it right now.
Added [URL="http://primes.utm.edu/primes/page.php?id=118016"]118016[/URL] : 653*10^1435026-1 (1435029 digits)[/QUOTE]

42nd on the list! Very impressive! :toot:

[QUOTE=paulunderwood;375707]Congrats!? You really should prove it before submission to the top5000 :rant:[/QUOTE]

I'd guess the first test proved it (i.e. it was an N+1, not a PRP test). As long as we have no reason to doubt the integrity of the test (e.g. experimental software), and the test wasn't just PRP, and the prime isn't mainstream-news-worthy (e.g. new Mersenne), I'm not against submitting it without a double check.
Basically, my impression from the notes and warnings at [url]http://primes.utm.edu/primes/submit.php[/url] is that [I]you[/I] should be convinced that it is proven prime before submitting it.

[QUOTE=unconnected;375706]Can't wait another day to complete N+1 test. So I submit it right now.
Added [URL="http://primes.utm.edu/primes/page.php?id=118016"]118016[/URL] : 653*10^1435026-1 (1435029 digits)[/QUOTE]
Very berry nice! :tu:
And a near rep-unit, too; let [URL="http://homepage2.nifty.com/m_kamada/math/factorizations.htm"]Kamada[/URL] know, he will be thrilled!

[QUOTE=Batalov;375718]Very berry nice! :tu:
And a near rep-unit, too; let [URL="http://homepage2.nifty.com/m_kamada/math/factorizations.htm"]Kamada[/URL] know, he will be thrilled![/QUOTE]

The number is 6529999.....9, which doesn't quite meet any of the named categories I see at the link, since it has exactly three digits different.

[QUOTE=Mini-Geek;375721]The number is 6529999.....9, which doesn't quite meet any of the named categories I see at the link, since it has exactly three digits different.[/QUOTE]
It fits. M.Kamada collects any [URL="http://mada.la.coocan.jp/nrr/prime/primedifficulty.txt"]near- and far- repdigits[/URL], including e.g. 13190078378725094213765678546*10^n-1 (how about his one ;-)

[QUOTE=unconnected;375706]Can't wait another day to complete N+1 test. So I submit it right now.
Added [URL="http://primes.utm.edu/primes/page.php?id=118016"]118016[/URL] : 653*10^1435026-1 (1435029 digits)[/QUOTE]

A HUGE congrats on not only CRUS's largest proof but in shattering the project prime size record by more than 50%. WOW!! The huge primes really do come in triplet on this project. A party is in order:
:bounce wave::groupwave::george::et_::curtisc:


[QUOTE=paulunderwood;375707]Congrats!? You really should prove it before submission to the top5000 :rant:[/QUOTE]

[I]Congrats!? [/I]with a question mark? What's up with that? I disagree with this statement. If a strong PRP test has been run, then it's OK to submit it as prime to the top-5000 while waiting for the primality proof. The reason: There is a greater chance of being struck by lightning 3 times in one day than a strong PRP of this size being composite. I have submitted > 5 PRPs to top-5000 that were still waiting on their primality proof on my machine. There is no reason to delay the inevitable with the small exception mentioned by Tim (Mini-Geek): If there is a big media announcement about the prime.


[QUOTE=rogue;375711]Is this in the right thread? That doesn't appear to be found as part of this project.

Congrats nonetheless.[/QUOTE]

Congrats [I]nonetheless[/I]??? "Nonetheless"...surely you jest. Come on people! What's with the half-hearted congrats? That's two of them now. This prime proves Riesel base 100, i.e.:
653*100^717513-1 is prime!

[QUOTE=Mini-Geek;375712]42nd on the list! Very impressive! :toot:

I'd guess the first test proved it (i.e. it was an N+1, not a PRP test). As long as we have no reason to doubt the integrity of the test (e.g. experimental software), and the test wasn't just PRP, and the prime isn't mainstream-news-worthy (e.g. new Mersenne), I'm not against submitting it without a double check.
Basically, my impression from the notes and warnings at [URL]http://primes.utm.edu/primes/submit.php[/URL] is that [I]you[/I] should be convinced that it is proven prime before submitting it.[/QUOTE]

I still disagree. IMHO It is OK to submit huge strong PRPs to top-5000 that are in the process of being proven (and it is known that they can be proven, i.e. of the form k*b^n-1 or k*b^n+1) if the chance of it not being prime is less than the chance of getting struck by lightning 3 times in one day. lol Regardless, it is nice to know that it had already been proven by an N+1 primality test. Doublechecking before submission is complete overkill unless the media would become involved.

Or perhaps I digress and agree: Based on Tim's last sentence here from a posting on top-5000. For a PRP of this size, I [I]would be convinced[/I] that it is a prime after a strong PRP test so IMHO, that is justification enough for submitting it.

I'm looking forward to seeing CRUS's and Dimitry's score make a huge jump at top-5000. Congrats again Dimitry! :smile: Edit: When the score is applied, we will be only about a score of 50 behind PSP for 5th place on the project score list!

My apologies on your find. I was thinking base 10, not base 100, so I didn't recognize this as proving the conjecture. I must say that I am just a wee bit jealous. :bow:

Well, you would never catch me submitting a PRP for proof by The Prime Pages server. Reasons? There could have been hardware failure. It could be a Carmichael number. I like to be 99.99999 recurring per cent sure, not 99.9999.....9999% :ermm:

[CODE]Command: /home/caldwell/client/pfgw/pfgw64 -tp -q"653*10^1435026-1" 2>&1
PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11]
Primality testing 653*10^1435026-1 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 3, base 1+sqrt(3)
Calling Brillhart-Lehmer-Selfridge with factored part 69.90%


653*10^1435026-1 is prime! (42902.6019s+0.0287s)
[Elapsed time: 11.92 hours][/CODE]

:party:

N+1 test on my side was finished few minutes ago.
[QUOTE]Primality testing 653*10^1435026-1 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 3, base 1+sqrt(3)
653*10^1435026-1 is prime! (293303.4768s+0.0688s)
[/QUOTE]

[QUOTE=paulunderwood;375746]Well, you would never catch me submitting a PRP for proof by The Prime Pages server. Reasons? There could have been hardware failure. It could be a Carmichael number. I like to be 99.99999 recurring per cent sure, not 99.9999.....9999% :ermm:[/QUOTE]

It's possible, though exceedingly unlikely, that unnoticed software glitches or random bit flips could produce a "prime" result in a composite number. Sorry, but you're still dealing with 99.9999.....9999%. The only difference is how many 9's there are (and how mathematically quantifiable that is).

I'd be more inclined to "trust" a number that's passed multiple PRP tests (especially multiple types) than a number that's passed a single deterministic primality test.

99.9 recurring per cent only occurs in theory. In practice, we're only 99.9999.....9999% sure that M57885161 is prime. (granted, this number is close enough to 100% that we, in practice, treat it as 100%)

Also, vaguely on the topic of proving primes: [URL="http://www.mersenneforum.org/showthread.php?t=19425"]LLR vs PFGW speed[/URL] In a quick test on my computer, LLR is [I]far[/I] better for proving this prime. I estimate that I can do it on one core of my CPU in ~7000 seconds (just under 2 hours).

[URL="http://mersenneforum.org/showthread.php?t=19142"]It had happened before[/URL], though. So it is a good thing to blow on cold water ([URL="http://translation.babylon.com/english/Once+burned+by+milk+you+will+blow+on+cold+water/"]Cf.[/URL]), just in case.

One thing that is implied in the above improbability arguments is that "let's say, a random bit flipped -- but the result is still random!" That's not what happens, at least in some implementations. If the whole interim residue is zeroed in (there are hardware failures that do that), then the rest of exponentiation will stay all zeroes. The end result is implementation dependent. P95 catches those zero-ins early, other programs - we don't know for sure (and who has time to read the source, right?).