Largest random prime

What is the largest prime generated more or less randomly, i.e. not having a particular special form, that has been proven prime with a general-purpose deterministic algorithm?

[Numbers]

In 1876, the French mathematician Edouard Lucas proved that 2^(127)-1 was prime. This was at the time the largest known prime number and remains the largest prime found without the aid of a computer.
Ever since then the largest known prime has always had one special form or another, so this number you are looking for is buried somewhere in about (and I’m guessing here) 20 millionth place on the list of the highest primes. Which means that unless someone cared to expend a lot of research time on trying to find it, it is almost certainly anonymous.
If you really, really have to know or you won’t be able to get to sleep, then you might try going here:

http://primes.utm.edu/

Chris Caldwell is widely acknowledged as an authority on this kind of question, and although he does not actively invite queries, he doesn’t bite; but unless he finds it interesting he might just ignore your question.

[Ken_g6]

This page lists the largest primes proven with ECPP, which is a general-purpose primality proving algorithm. That probably means the numbers on that page can't be proven prime because of their special form(s).

The largest one I see on that page that is not described with a special form comes from this page, and is a 7996-digit number.

[jinydu]

I guess a better way to formulate the question would be:

"What is the largest number to be proven prime using a primality proving algorithm that works for all positive integers?"

[cheesehead]

Originally Posted by jinydu

"What is the largest number to be proven prime using a primality proving algorithm that works for all positive integers

... but on which no known primality proving algorithm that requires a special form can be used

?"

[fatphil]

Originally Posted by Fredrik

What is the largest prime generated more or less randomly, i.e. not having a particular special form, that has been proven prime with a general-purpose deterministic algorithm?

Some have called these "entropic" primes. Ones for which no uniquely defining description can be shorter than just the number itself. The current, but perhaps invalid, record is held by David Broadhurst, but claims to invalidity were based on the fact that I believed that his numbers could possibly be compressed marginally (by a few bits out of several hundred thousand).

Unfortunately there's not really anything mathematically interesting about such numbers. Two calls to a random number generator are all you need, one to chose a factor for BLS/KP/CHG, and one to decide where to search for primes. Dirichlet guarantees there'll be something eventually.