The number

 (((((((((2^3+3)^3+30)^3+6)^3+80)^3+12)^3+450)^3+894)^3+3636)^3+70756)^3+97220

is prime. Interested readers may read

   http://www.cs.uwaterloo.ca/journals/JIS/VOL8/Caldwell/caldwell78.html

for the origin of this number.

It has 20,562 decimal digits and the proof was built using
fastECPP [1] on several networks of workstations. It was suggested as a
challenge for primality proving. Since machines are more available
than human time, letting them work for a somewhat unreasonnable amount
of time is not an issue, as long as only one human check is needed
from time to time. Thanks to stable power supply, and network, let
alone a stable program, this record was possible. The computations
were started on 32-bit machines (Sep-Oct 2005), and finished on nine
64-bit bi-processors (Feb-June 2006).

Cumulated timings are given w.r.t. AMD Opteron(tm) Processor 250 at
2.39 GHz.

1st phase: 1900 days (396 for sqrt; 384 for Cornacchia; 1353 for PRP tests)
2nd phase:  319 days (8 days for building all H_D's; 277 for solving H_D mod p)

The certificate (48Mb compressed) can be found at:

http://www.lix.polytechnique.fr/Labo/Francois.Morain/Primes/Certif/mills2.certif.gz

It took 10 days to check the 1765 proof steps on a single processor.

F. Morain

[1] http://www.lix.polytechnique.fr/Labo/Francois.Morain/Articles/fastecpp-final.ps.gz