## Re: nonprime?

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• ... to ... Using PFGW, I have found all those with
Message 1 of 10 , Mar 1, 2007
<paulunderwood@...> wrote:
>
to
> see gigantic PrPs:
>
> 9 2^505431-505431 152150 Henri Lifchitz 04/2005
> 10 2^500899-500899 150786 Henri Lifchitz 04/2005
> 11 2^481801-481801 145037 Henri Lifchitz 03/2005
> 108 2^228271-228271 68717 Henri Lifchitz 11/2004
> 170 2^182451-182451 54924 Henri Lifchitz 10/2004
> 509 2^108049-108049 32526 Henri Lifchitz 11/2001
> 2527 2^61011-61011 18367 Henri Lifchitz 09/2001
> 2534 2^60975-60975 18356 Henri Lifchitz 09/2001
> 5891 2^44169-44169 13297 Henri Lifchitz 09/2001
>
> There may be more sub-giantic ones,

Using PFGW, I have found all those with < 10000 digits:-

2^2-2 prime by PFGW
2^3-3 prime by PFGW
2^9-9 prime by PFGW
2^13-13 prime by PFGW
2^19-19 prime by PFGW
2^21-21 prime by PFGW

2^55-55 prime by PRIMO 0s
2^261-261 prime by PRIMO 0.06s
2^3415-3415 prime by PRIMO 47mn 6s
2^4185-4185 prime by PRIMO 2h 3mn 22s
2^7353-7353 prime by PRIMO 23h 20mn 22s
2^12213-12213 137-PRP by PFGW [PRIMO certification would take c. 6
days]

[
BTW when Werner said:
>2^n-n is prime for n=3415, 4185, 7353.
I think he was being optimistic, and should have said "probable
prime", no?
]

I've done the same for 2^n+n.

gives:

3 2^678561+678561 204268 Henri Lifchitz 05/2006
137 2^204129+204129 61449 Henri Lifchitz 04/2002
937 2^88071+88071 26513 Henri Lifchitz 09/2001

so the first of these is the 3rd-largest PRP known.

And to complete the picture, here are all those with < 10000 digits :-

2^1+1 prime by PFGW
2^3+3 prime by PFGW
2^5+5 prime by PFGW
2^9+9 prime by PFGW
2^15+15 prime by PFGW

2^39+39 prime by VFYPR 0 sec
2^75+75 prime by VFYPR 0 sec
2^81+81 prime by VFYPR 0 sec
2^89+89 prime by VFYPR 0 sec
2^317+317 prime by VFYPR 2 sec
2^701+701 prime by VFYPR 60 sec
2^735+735 prime by VFYPR 71 sec
2^1311+1311 prime by VFYPR 1484 sec
2^1881+1881 prime by VFYPR 11991 sec
2^3201+3201 prime by PRIMO 48mn 23s
2^3225+3225 prime by PRIMO 38mn 50s
2^11795+11795 137-PRP by PFGW (PRIMO certification would take c. 5
days)

All timings are for a 1.2 GHz PC.

Anyone want to do those 2 bigger certifications with PRIMO?

-Mike Oakes
• Hi, ... It took a bit less than 4 (CPU) days on my PC, but since I can only run it during working hours, and I took a week off, it took quite some (wall-clock)
Message 2 of 10 , Mar 23, 2007
Hi,

On 3/2/07, Mike Oakes <mikeoakes2@...> wrote:
> 2^12213-12213 137-PRP by PFGW [PRIMO certification would take c. 6
> days]

It took a bit less than 4 (CPU) days on my PC, but since I can only
run it during working hours, and I took a week off, it took quite some
(wall-clock) time...

[PRIMO - Primality Certificate]
Version=2.3.1
WebSite=http://www.ellipsa.net/
Format=3
ID=B2E4101C81D29
Created=03-02-2007 08:18:24 am
TestCount=498
Status=Candidate certified prime

[Running Times]
Initialization=11.70s
1stPhase=73h 34mn 19s
2ndPhase=21h 45mn 27s
Total=95h 19mn 58s

[Candidate]
File=C:\Christ\Primo 2.3.1\2^y-y.in
Expression=2^12213-12213

I'll start testing the + form Mike mentioned on Monday.

The full cert will be published and checked soon.

Have a good week-end!

Christ van Willegen
• Hi, Mike Oakes said: 2^11795+11795 137-PRP by PFGW (PRIMO certification would take c. 5 days) My computer says: [PRIMO - Task Report] Version=2.3.1
Message 3 of 10 , Apr 10, 2007
Hi,

Mike Oakes said:
2^11795+11795 137-PRP by PFGW (PRIMO certification would take c. 5
days)

My computer says:
Version=2.3.1
WebSite=http://www.ellipsa.net/
ID=B2E63036D59E4
Created=04-05-2007 03:58:18 pm

[Common]
Path=C:\Christ\Primo 2.3.1\
Selected=1
Processed=1
Certified=1
Candidate #1=Certified, 94h 3mn 48s

[Candidate #1]
Input=primo-B2E5901A2ECA1-001.tmp
Report=primo-B2E5901A2ECA1-001.cr
Output=primo-B2E5901A2ECA1-001.out
Status=Candidate certified prime

So, both numbers have been proven prime.

I'll run Cert_val on the second certificate and publish both after that.

Christ van Willegen
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