> This is a complete list of prp's of the form a^b+b^a, where

List deleted.

> 1<a<b<1001:

> 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- Phil Carmody wrote:

> I noticed that 3 of the entries in the

Hmm... a^(a-1)+(a-1)^a doesn't look circle cutting

> a^b+b^a list had a=b+1.

(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!

Christ wan Willegen wrote:

>I have no prior Titanix experience, but I think it's time

for me

>to give it a try...

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

>

>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.

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.

Waiting for comments.

Best wishes,

Andrey

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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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