Ok, thanks for explaining that. It sounds like the condition for notability in this case is the combination of size and algorithm used?
> Carmody created a 1905-digit prime, of the form k·256211 + 99, that was the tenth largest prime found using ECPP, a remarkable achievement by itself and worthy of being published on the lists of the highest prime numbers.
Oh, I didn't realize the page said that. I should have read it more carefully. You're right that it's a combination of size and method used. The Mersenne numbers are especially easy to prove prime, so it's also interesting to keep track of the largest primes proved by other methods. I think these days a 2000 digit prime wouldn't be notable in any case, but it sounds like it was back when Carmody was doing this, so this was in fact a good example of an illegal number that was independently interesting.
