## Re: [PrimeNumbers] Second mega-trit prime

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• ... Two in such a short time. Great finds, David! --Mark [Non-text portions of this message have been removed]
Message 1 of 16 , Feb 13, 2010
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On Feb 13, 2010, at 5:30 PM, djbroadhurst wrote:

>
> Running N-1 test using base 2
> Calling Brillhart-Lehmer-Selfridge with factored part 100.00%
> 2*3^1086112+1 is prime! (4856.6481s+0.0729s)
>
> But I would rest easier if Jean can confirm it with LLR.
> It was a bit weird getting two in two days:
>
> David, pp SCRUB,
> Society for the Comfort and Relief of Underprivileged Bases

Two in such a short time. Great finds, David!

--Mark

[Non-text portions of this message have been removed]
• What a beautiful double success !! I tested the first this night : ~/llr380src/linuxllr \$ ./llr -d -q 2*3^1074726+1 Base prime factor(s) taken : 3 Starting
Message 2 of 16 , Feb 13, 2010
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What a beautiful double success !!

I tested the first this night :

~/llr380src/linuxllr \$ ./llr -d -q"2*3^1074726+1"
Base prime factor(s) taken : 3
Starting N-1 prime test of 2*3^1074726+1
2*3^1074726+1 may be prime, trying to compute gcd's
2*3^1074726+1 may be prime, but N divides 3^((N-1)/3))-1, restarting with a=5 Time : 7320.190 sec.
Restarting N-1 prime test of 2*3^1074726+1
2*3^1074726+1 may be prime, trying to compute gcd's
5^((N-1)/3)-1 is coprime to N!
2*3^1074726+1 is prime! Time : 8911.548 sec.

It seems I was a bit more lucky than OpenPFGW while finding a primitive root base... Do you know a mean not to be submitted only to luck about this search?

I shall now verify the second (mainly to test the young new LLR, I am confident it is prime!)

Many congratulations, and Best Regards,
Jean

--- In primenumbers@yahoogroups.com, Mark Rodenkirch <mgrogue@...> wrote:
>
>
> On Feb 13, 2010, at 5:30 PM, djbroadhurst wrote:
>
> >
> > Running N-1 test using base 2
> > Calling Brillhart-Lehmer-Selfridge with factored part 100.00%
> > 2*3^1086112+1 is prime! (4856.6481s+0.0729s)
> >
> > But I would rest easier if Jean can confirm it with LLR.
> > It was a bit weird getting two in two days:
> >
> > David, pp SCRUB,
> > Society for the Comfort and Relief of Underprivileged Bases
>
> Two in such a short time. Great finds, David!
>
> --Mark
>
> [Non-text portions of this message have been removed]
>
• ... Thank you, kindly, dear Sir. I am much relieved. ... It was the second that made me worry: too much of a good thing , I said to myself, with my usual
Message 3 of 16 , Feb 14, 2010
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"jpyah2001" <jpenne@...> wrote:

> 2*3^1074726+1 is prime! Time : 8911.548 sec.

Thank you, kindly, dear Sir. I am much relieved.

> I shall now verify the second (mainly to test the young
> new LLR, I am confident it is prime!)

It was the second that made me worry:
"too much of a good thing", I said to myself,
with my usual skepticism.

So another test by "young new LLR" would be
much appreciated, even though it does now
look as if it indeed may succeed.

As ever, I rely on the existence of a variety
of software, with dedicated and generous authors
and maintainers, to keep us free of needless error.

David
• It is prime, indeed!! ./llr -d -q 2*3^1086112+1 Base prime factor(s) taken : 3 Starting N-1 prime test of 2*3^1086112+1 2*3^1086112+1 may be prime, trying to
Message 4 of 16 , Feb 14, 2010
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It is prime, indeed!!

./llr -d -q"2*3^1086112+1"
Base prime factor(s) taken : 3
Starting N-1 prime test of 2*3^1086112+1
2*3^1086112+1 may be prime, trying to compute gcd's
3^((N-1)/3)-1 is coprime to N!
2*3^1086112+1 is prime! Time : 7392.541 sec.

Bravo!
Jean

>
>
>
> "jpyah2001" <jpenne@> wrote:
>
> > 2*3^1074726+1 is prime! Time : 8911.548 sec.
>
> Thank you, kindly, dear Sir. I am much relieved.
>
> > I shall now verify the second (mainly to test the young
> > new LLR, I am confident it is prime!)
>
> It was the second that made me worry:
> "too much of a good thing", I said to myself,
> with my usual skepticism.
>
> So another test by "young new LLR" would be
> much appreciated, even though it does now
> look as if it indeed may succeed.
>
> As ever, I rely on the existence of a variety
> of software, with dedicated and generous authors
> and maintainers, to keep us free of needless error.
>
> David
>
• ... Here s a third, according to OpenPFGW: Primality testing 2*3^1175232+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Running N-1 test
Message 5 of 16 , Feb 22, 2010
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"jpyah2001" <jpenne@...> wrote:

> 2*3^1086112+1 is prime! Time : 7392.541 sec.

Here's a third, according to OpenPFGW:

Primality testing 2*3^1175232+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 2
Running N-1 test using base 3
Calling Brillhart-Lehmer-Selfridge with factored part 100.00%
2*3^1175232+1 is prime! (12689.9371s+0.0402s)

David
• ... I am trying to learn to count in Telefol, which uses base 27. http://en.wikipedia.org/wiki/Telefol_language ... The first 27 positive integers are
Message 6 of 16 , Feb 26, 2010
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> 2*3^1175232+1 is prime! (12689.9371s+0.0402s)

I am trying to learn to count in Telefol, which uses base 27.

http://en.wikipedia.org/wiki/Telefol_language
> Telefol is a language spoken by the Telefol people in Papua
> New Guinea, notable for possessing a base-27 numeral system.

The first 27 positive integers are signalled like this:

01--05: left small finger to left thumb
06--10: left wrist, ulna, elbow, humerus, shoulder
11--13: left side of neck, left ear, left eye
14--14: nose
15--17: right eye, right ear, right side of neck
18--22: right shoulder, humerus, elbow, ulna, wrist
24--27: right thumb to right small finger

If we then adopt place value, the right small finger also
serves as our zero, in base 27. So you have more than
333,333 exercises on that finger, to signal one of the three
known mega-trit primes. Now it so happens that I have a
severe Dupuytren contracture of my right small finger, so my
position of Secretary of SCRUB has now become quite
challenging.

David, pp SCRUB
Society for the Comfort and Relief of Underprivileged Bases,
Main Office: Telefomin District, Sandaun Province, Papua New Guinea
• ... SCRUB wishes to apologize to speakers of Hewa, Oksapmin, Orokolo, Sanio and Tifal, for having previously omitted to mention that they also count in base
Message 7 of 16 , Feb 26, 2010
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> I am trying to learn to count in Telefol, which uses base 27.

SCRUB wishes to apologize to speakers of Hewa, Oksapmin,
Orokolo, Sanio and Tifal, for having previously omitted
to mention that they also count in base 27, as shown here:
http://www.uog.ac.pg/glec/counting_sys/t-coutning_sys/t-counting_sys.htm

David, pp SCRUB
Society for the Comfort and Relief of Underprivileged Bases
• Many congrats for this third success! But, this time LLR needed one more restart... ... Base prime factor(s) taken : 3 Starting N-1 prime test of 2*3^1175232+1
Message 8 of 16 , Mar 1, 2010
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Many congrats for this third success!

But, this time LLR needed one more restart...

>cllr -d -a68 -q"2*3^1175232+1"
Base prime factor(s) taken : 3
Starting N-1 prime test of 2*3^1175232+1
Using all-complex FFT length 96K, a = 3
2*3^1175232+1 may be prime, trying to compute gcd's
2*3^1175232+1 may be prime, but N divides 3^((N-1)/3))-1, restarting with a=5 Time : 8983.686 sec.
Restarting N-1 prime test of 2*3^1175232+1
Using all-complex FFT length 96K, a = 5
2*3^1175232+1 may be prime, trying to compute gcd's
5^((N-1)/3)-1 is coprime to N!
2*3^1175232+1 is prime! Time : 8834.941 sec.

Best Regards,
Jean

>
>
>
> "jpyah2001" <jpenne@> wrote:
>
> > 2*3^1086112+1 is prime! Time : 7392.541 sec.
>
> Here's a third, according to OpenPFGW:
>
> Primality testing 2*3^1175232+1 [N-1, Brillhart-Lehmer-Selfridge]
> Running N-1 test using base 2
> Running N-1 test using base 3
> Calling Brillhart-Lehmer-Selfridge with factored part 100.00%
> 2*3^1175232+1 is prime! (12689.9371s+0.0402s)
>
> David
>
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