According to the Onrejka-Dubner-Dubner tables at
http://www.utm.edu/research/primes/lists/top_ten/

3(5)_{1973}3 = 32*(10^1974-1)/9+1

was the largest proven plateau prime known in May 2001.
In base 10, it consists of 1973 successive 5's
sandwiched by a pair of 3's.

It was rather easy to improve on this. OpenPfgw gave

> Primality testing 4*(10^2898-1)/3-1
> [N+1, Brillhart-Lehmer-Selfridge]
> Calling Brillhart-Lehmer-Selfridge with factored part 33.46%
> 4*(10^2898-1)/3-1 is prime!

which proves that

1(3)_{2897}1 = 4*(10^2898-1)/3-1

is a 2899-digit plateau prime, consisting of 2897
successive 3's sandwiched by a pair of 1's.

I also investigated the following larger plateau PrPs

1(3)_{3093}1 = 4*(10^3094-1)/3-1
1(3)_{3111}1 = 4*(10^3112-1)/3-1
3(7)_{3379}3 = 34*(10^3380-1)/9-1
3(7)_{3875}3 = 34*(10^3876-1)/9-1
3(7)_{5207}3 = 34*(10^5208-1)/9-1
3(5)_{7229}3 = 32*(10^7230-1)/9+1

with factorizations of N^2-1 enabled by
http://groups.yahoo.com/group/primenumbers/files/Factors/hd.zip
but each appears to need more ECM work before one can
achieve even a Konyagin-Pomerance proof, at 30% factorization.

Some of the above might make appropriate targets for
cyclotomy-assisted APRCL effort, if Jason Moxham and/or
Phil Carmody ever get the urge.

Patrick de Geest found that

3(7)_{10745}3 = 34*(10^10746-1)/9-1
1(3)_{15697}1 = 4*(10^15698-1)/3-1
1(3)_{17955}1 = 4*(10^17956-1)/3-1

are PrPs, but these don't seem promising either.

See Patrick's page
http://www.worldofnumbers.com/pdpsorted.htm
for other plateau PrPs that might serve as
ECPP targets, unaided by N^2-1 cyclotomy.

David Broadhurst