Xinyao Chen informs me (May 19,2022) that this number
(10^10906*64+53)/9 is now a proven plateau-and-depression prime.
See http://factordb.com/index.php?id=1000000000008860930.
Proof was done by Jens Kruse Andersen on October 17, 2002 (certified by: Greg Childers / PRIMO / May 18, 2022).
Certificate at https://stdkmd.net/nrr/cert/7/#CERT_71117_10906.

By Serge Batalov dd. March 1, 2015.

(64*10^499210+53)/9 is base 3-Strong Fermat PRP! (499211 decimal digits)  Time : 4225.750 sec.

Tools : srsieve.