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## Re: [PrimeNumbers] a^b+b^a is PRP!

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• ... You might want to try that yourself. You d be surprised at the speed at which Titanix can prove primes with less than 2000 digits. There are a few larger
Message 1 of 13 , Jun 1, 2001
--- Andrey Kulsha <Andrey_601@...> wrote:
> Hello!
>
> This is a complete list of prp's of the form
> a^b+b^a, where
> 1<a<b<1001:
>
>
> Does anybody want to prove some of them prime via
> Titanix?

You might want to try that yourself. You'd be
surprised at the speed at which Titanix can prove
primes with less than 2000 digits. There are a few
larger than that that will take a little more time.

If I had the time I would help you out but to busy
right now with Lucas and Fibonacci business.

Bouk.

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• ... I d have to say (based on my limited knowledge) a LOT of time. A rough mental estimate using logs seems to indicate that some of his numbers are in the
Message 2 of 13 , Jun 1, 2001
On Fri, 1 Jun 2001 19:13:07 -0700 (PDT), Bouk wrote:

>
>--- Andrey Kulsha <Andrey_601@...> wrote:
>> Hello!
>>
>> This is a complete list of prp's of the form
>> a^b+b^a, where
>> 1<a<b<1001:
>>
>>
>> Does anybody want to prove some of them prime via
>> Titanix?
>
>You might want to try that yourself. You'd be
>surprised at the speed at which Titanix can prove
>primes with less than 2000 digits. There are a few
>larger than that that will take a little more time.

I'd have to say (based on my limited knowledge) a LOT of time.

A rough mental estimate using logs seems to indicate that some of his
numbers are in the range of nine thousand digits (though I could be
off by a fair amount there). I didn't know such numbers were even
close to being proveable at present.

Of course, I might be in error on that.

Nathan
• If I am correct none of the prp s has more than 3000 decimal digits which makes them all provable by Titanix in a sensible amount of time. 9000 digits would
Message 3 of 13 , Jun 2, 2001
If I am correct none of the prp's has more than 3000
decimal digits which makes them all provable by
Titanix in a sensible amount of time.

9000 digits would indeed be way too large. Titanix can
handle such numbers but to prove them would take ages.
Real ages ;-)

Bouk.

--- Nathan Russell <nrussell@...> wrote:
> On Fri, 1 Jun 2001 19:13:07 -0700 (PDT), Bouk wrote:
>
> >
> >--- Andrey Kulsha <Andrey_601@...> wrote:
> >> Hello!
> >>
> >> This is a complete list of prp's of the form
> >> a^b+b^a, where
> >> 1<a<b<1001:
> >>
> >>
> >> Does anybody want to prove some of them prime via
> >> Titanix?
> >
> >You might want to try that yourself. You'd be
> >surprised at the speed at which Titanix can prove
> >primes with less than 2000 digits. There are a few
> >larger than that that will take a little more time.
>
> I'd have to say (based on my limited knowledge) a
> LOT of time.
>
> A rough mental estimate using logs seems to indicate
> that some of his
> numbers are in the range of nine thousand digits
> (though I could be
> off by a fair amount there). I didn't know such
> numbers were even
> close to being proveable at present.
>
> Of course, I might be in error on that.
>
> Nathan
>
> Unsubscribe by an email to:
> The Prime Pages : http://www.primepages.org
>
>
>
> Your use of Yahoo! Groups is subject to
> http://docs.yahoo.com/info/terms/
>
>

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• Hello! ... Yes, I know: 2057-digit prime took less than 4 days on Duron-700 with Titanix 2.0.4b, so on Athlon-1200 all these prp s can be proven in 2 weeks or
Message 4 of 13 , Jun 2, 2001
Hello!

Bouk de wrote:

>You might want to try that yourself. You'd
>be surprised at the speed at which Titanix
>can prove primes with less than 2000 digits.
>There are a few larger than that that will
>take a little more time.

Yes, I know: 2057-digit prime took less than 4 days on
Duron-700 with Titanix 2.0.4b, so on Athlon-1200 all these
prp's can be proven in 2 weeks or so...

But my computer has AMD K6-233 processor... :-(

So I think it will be better if someone with faster machine
prove them prime. Of course, he will be a 100% prover.

Thanks,

Andrey
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• Hi, ... I have no prior Titanix experience, but I think it s time for me to give it a try... Andrey, I am willing to use my Athlon-800 for a few days to try to
Message 5 of 13 , Jun 2, 2001
Hi,

> Bouk de wrote:
>
> >You might want to try that yourself. You'd
> >be surprised at the speed at which Titanix
> >can prove primes with less than 2000 digits.
> >There are a few larger than that that will
> >take a little more time.
>
> Yes, I know: 2057-digit prime took less than 4 days on
> Duron-700 with Titanix 2.0.4b, so on Athlon-1200 all these
> prp's can be proven in 2 weeks or so...
>
> But my computer has AMD K6-233 processor... :-(
>
> So I think it will be better if someone with faster machine
> prove them prime. Of course, he will be a 100% prover.

I have no prior Titanix experience, but I think it's time for me
to give it a try...

Andrey, I am willing to use my Athlon-800 for a few days
to try to prove them. Select a few large ones, so that I
will be busy for a week or so. You yourself (or someone
else?) can perhaps take the smaller ones.

Just send me them off-list. I don't know if you have any time
for coordinating this search, but the list doesn't look overly
long, so perhaps you'd be able to distribute things
yourself.

Regards,

Christ van Willegen
• ... Phil the mod might sleep easier on his bus if combined efforts resulted in 5 ECPP primes with more than 1905 digits. Then the illegal part of Chris
Message 6 of 13 , Jun 2, 2001
Christ van Willegen wrote:
> Select a few large ones, so that I
> will be busy for a week or so.
Phil the mod might sleep easier on his bus
if combined efforts resulted in 5 ECPP primes
with more than 1905 digits. Then the illegal
part of Chris Caldwell's database will disappear.

ECPP top-16:

(348^1223-1)/347 3106
(30^1789-1)/29 2642
(2^7757-1)/233....361 2303
(((((1361^3+....+894)^3+3636 2285
(2^7331-1)/458072843161 2196
Phi(4274,10) 2136
(2^7039-1)/(125...721) 2074
100^1013-99^1013 2026
U(9677) 2023
V(20460) 2007
4915416*10^1999+19 2006
4915416*10^1999+17 2006
10^1999+7321 2000
Phi(3927,10) 1920
(10^1918-7)/3 1918
'css_descramble.c.gz'*256^211+99 1905

Indeed, folk out there might already have 2k+ digits
Tx proofs that they have forgotten to post. If so,
just submit the prime with the comment ECPP.
• ... I forgot to add: if you do not have a code with Titanix in it, ask Chris Caldwell for a c? code, so Marcel get recognized. (c is the first first letter of
Message 7 of 13 , Jun 2, 2001
I wrote:

> Indeed, folk out there might already have 2k+ digits
> Tx proofs that they have forgotten to post. If so,
> just submit the prime with the comment ECPP.

I forgot to add: if you do not have a code with Titanix
in it, ask Chris Caldwell for a c? code, so Marcel
get recognized. (c is the first first letter of Titanix :-)

David
• ... Mod? _Mod_? Never has a rocker been so offended! (Yeah, yeah, I know what you meant.) Anyway, I was just curious - I noticed that 3 of the entries in the
Message 8 of 13 , Jun 2, 2001
On Sat, 02 June 2001, d.broadhurst@... wrote:
> Christ van Willegen wrote:
> > Select a few large ones, so that I
> > will be busy for a week or so.
> Phil the mod might sleep easier on his bus

Mod? _Mod_? Never has a rocker been so offended!
(Yeah, yeah, I know what you meant.)

Anyway, I was just curious - I noticed that 3 of the entries in the a^b+b^a list had a=b+1. Are there any witty decompositions of N-1 which could provide a BLS proof to this case?
A was able to find the factor b by hand, but are there any others?

Dues to mystical magical exploding computers I am without Mathematica presently, and unable to do symbolic mathematics!

(Anyone know of a free symbolic maths tool?)

I threw the 80/81 number at ECM, and split >33% of it, but that could be pure coincidence!

Hmmm, back to work :-(

Phil

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• ... List deleted. ... I posted to this very forum exactly the same list on Thursday 22nd February under the Subject: Primes and strong pseudoprimes of the
Message 9 of 13 , Jun 2, 2001
> This is a complete list of prp's of the form a^b+b^a, where
> 1<a<b<1001:

List deleted.

> Does anybody want to prove some of them prime via Titanix?

I posted to this very forum exactly the same list on Thursday 22nd
February under the Subject: "Primes and strong pseudoprimes of the form
x^y+y^x". I can repost if wished, but assume that readers know how to
examine the list archives. That post also included the pair (1015,384).
Somewhere, still not found but probably on a backup tape, the list
continues to about 1500 or so.

Many of the primes were proved by me years ago, and I had two in the
prime record tables until they were re-catalogued as uninteresting.

I'd be interested in seeing some of them proved prime --- the ones I
never got around to completing!

Paul
• ... Hmm... a^(a-1)+(a-1)^a doesn t look circle cutting (cyclotomic) from here. I think cyclotomy is always a^n-b^n (and if you want the full Monty, set
Message 10 of 13 , Jun 2, 2001
Phil Carmody wrote:

> I noticed that 3 of the entries in the
> a^b+b^a list had a=b+1.

Hmm... a^(a-1)+(a-1)^a doesn't look circle cutting
(cyclotomic) from here. I think cyclotomy is always
a^n-b^n (and if you want the full Monty, set
a=(1+sqrt(5))/2 and b=(1-sqrt(5))/2)
and divide by a-b=sqrt(5) to get a well known integer)

David
• Hello! ... for me ... Well, I may prove the numbers which have
Message 11 of 13 , Jun 2, 2001
Hello!

Christ wan Willegen wrote:

>I have no prior Titanix experience, but I think it's time
for me
>to give it a try...
>
>Andrey, I am willing to use my Athlon-800 for a few days
>to try to prove them. Select a few large ones, so that I
>will be busy for a week or so. You yourself (or someone
>else?) can perhaps take the smaller ones.

Well, I may prove the numbers which have <=1000 digits.

But:

Paul Leyland wrote:

>Many of the primes were proved by me years ago, and I had
two in the
>prime record tables until they were re-catalogued as
uninteresting.

Paul, please send us a list of primes you have proven, and
we'll prove all remaining ones.

I will prove less than 1000 digit numbers, Christ wan
Willegen, for example, will prove numbers with 1001..2000
digits, and someone third (maybe Paul Leyland) will prove
numbers with >2000 digits.

Note that 1000-digit prime 289^406+406^289 was proven by
Paul, and then independently by me as the smallest titanic
prime of such a kind. The primes 342^343+343^342,
111^322+322^111, 122^333+333^122, 8^69+69^8 was also proven
by me nearly 5 months ago; 365^444+444^365 was proven by me
and Marcel Martin (he found a step with record polynomial
degree of 100) nearly 3 months ago.

Best wishes,

Andrey
---------------------------------------------------
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• Hello! OK, I ll prove all remaining prps with less than 1200 digits, i.e.: 8^519+519^8, 20^471+471^20, 5^1036+1036^5, 56^477+477^56, 98^435+435^98,
Message 12 of 13 , Jun 4, 2001
Hello!

OK, I'll prove all remaining prps with less than 1200
digits, i.e.:

8^519+519^8,
20^471+471^20,
5^1036+1036^5,
56^477+477^56,
98^435+435^98,
21^782+782^21,
32^717+717^32,
365^444+444^365,
423^436+436^423,
34^773+773^34.

Best wishes,

Andrey
--------------------------------------------------
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