RE: [PrimeNumbers] a^b+b^a is PRP!
> This is a complete list of prp's of the form a^b+b^a, whereList 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!
- Phil Carmody wrote:
> I noticed that 3 of the entries in theHmm... 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)
Christ wan Willegen wrote:
>I have no prior Titanix experience, but I think it's timefor 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.
Paul Leyland wrote:
>Many of the primes were proved by me years ago, and I hadtwo in the
>prime record tables until they were re-catalogued asuninteresting.
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.
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OK, I'll prove all remaining prps with less than 1200
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