> But here is the big problem: definition.

You may wish to consider what the factoring community does in analgous cases.

>

> What makes a prime N an "ECPP" (or "Cyclotomy" or

> "Konyagin/Pomerance") prime? What if enough prime

> factors of N+/-1 are discovered later for more

> classical methods--does it lose the "ECPP"...?

> What if it is possible, but not obvious how, to use a

> simpler method and the prime is submitted as ECPP

> soon after to be done another way?

It's occasionally the case that a factorization is found by two methods essentially simultaneously. Most commonly, an ECM run spits out a small factor when a NFS or QS computation is still sieving, though other circumstances are occasionally found. For instance, Paul Zimmermann found a factor by P+1 of 118*^10^118+1 just after I'd started a SNFS run.

A similar circumstance occurs when a factor which is found by one method is found to be discoverable by another. I don't mean trivial cases such as using Pollard rho rather than trial division to find 8-digit factors but, rather, ECM discovering a factor which could have been found more quickly by P-1 or P+1. An extreme case and, admittedly, a contrived case was found in Simon Singh's Cipher challenge where a factorization of a 512-bit integer actually performed by GNFS could have been done in about 1% of the computation by P-1.

The factoring community invariably records the first reported method in these cases.

Paul> ECPP, Cyclotomy, Konyagin/Pomerance

1) ECPP is at present an archivable class, with a top-20.

I believe that it should stay like this, with Chris trying to

chase up the folk in Marcel's top-20 who are not yet in his.

Once proven by ECPP, no subsequent easier validation can demote

such a prime, since the top-20 is for primes first proven by ECPP.

2) Cyclotomy is at present an archivable class, with a top-20.

I believe that should be relegated to a mere comment.

No-one will be affected since all of the present top-20 are archivable

according to their mathematical definitions, irrespective of their

proof method.

3) Konyagin/Pomerance is at present neither an archivable class

nor an accepted comment.

I believe it should stay like this.

If folk want to indicate that KP was the proof method they can do

so as I do, using the <url,...,notes> addendum.

David Broadhurst> 1) ECPP is at present an archivable class, with a top-20.

Maybe Marcel could try to encourage his top-20 to contact Chris?

> I believe that it should stay like this, with Chris trying to

> chase up the folk in Marcel's top-20 who are not yet in his.

Congrats to Jeff Heleen:

http://www.ellipsa.net/pages/primotop20.html

(10^4769 - 1) / 3 - 2*10^2384

4769 decimal digits

Certified by Jeff Heleen (2002)

* Running time: 1464h

* Processor: AMD Athlon 1.3 GHz

David