(10^10683+11)/3
(10^12891+11)/3
(10^14118+11)/3

Those 3 PRPs were submitted by me in october 2008.
In 2010 Serge Batalov proved the middle one to be prime.
The other two remain unproved as of Feb 2012 according to

http://physics.open.ac.uk/~dbroadhu/cert/gigantic.txt

So I am resubmitting them

To be completed...