Landon Curt Noll told me the story of this. See
http://www.isthe.com/chongo/tech/math/prime/37.html
http://magliery.com/37/notes/primes.html
Here are some details from Landon, with permission.
<< The primality was established on a special hardware
system. This system was a black-box hardware designed for a
special customer. They wanted a system that had a growth
roadmap capable of reaching numbers as high as 2^10000. This
black-box was an add-on hardware to a Cray. The system
implemented n +/- 1 tests, ECPP, a Cyclotomy related test
as well as some others as I recall.
During hardware checkout, I was asked to advise on selected
matters. One day I came across Tom's amusing 37 page.
On a whim, and as a favor to Tom Magliery I submitted some
37-related candidates for testing. One of them,
(37*10^2883-73)/99 was just under the limit of the system.
Being highly probable, I asked that it be selected as one of
the test verification candidates.
Sometime later, I was told that (37*10^2883-73)/99 was
proven by the system. When I asked for details I was told
that the system proved primality two different ways. It was
strongly hinted that ECPP was used. When I asked about the
other successful test I received an answer that suggested
that a Cyclotomy related test was used as well. They did
say that I'd find it amusing that the Cray setup time for
the problem was 37 minutes of CPU time during a 37 hour
clock time run (setting up other tests). This setup time,
however, said nothing about how long the actual tests took.
Nor did it tell me which tests required such a long setup
time. When I pressed for more details such as actual test
run times, the date of the first proof or which test was
used first I was met with silence.
By that time the customer had already received the system.
Due to the nature of this customer, it was impossible to ask
for additional information.
So ... armed with this information I sent a message to Tom:
http://magliery.com/37/notes/primes.html
I opted to leave out the bit about the special hardware, due
to the nature of the customer. I did imply the 37 CPU
minutes on the Cray stretched out to 37 hours ... but gave
no exact detailed for obvious reasons.
Recently there has been renewed interest in this result.
I'm VERY embarrassed to say that I didn't pay much attention
to such a small but otherwise beautiful result when the
primality success was first reported back to me. I think
this was near the time when the ''large prime list'' limit
was raised from 1000 digits to 10000 digits ... perhaps this
is part of the reason that I ignored this result. Anyway
for whatever reason I did not think it worth mentioning a
2883 digit prime to anyone beyond the Tom. None of the
37-results were never published. Sorry!
Perhaps this is as a result of dealing with too many huge
primes? :-)
So, to the best of my ability:
The number was proven prime via ECPP: of that I am fairly
certain.
The number may have also been proven prime via a Cyclotomy
test as well: of that I reasonably certain.
To my knowledge this result has never been independently
verified although I recall someone hinted that they were
attempting it. >>
David's comment: It is rather impressive that this
undisclosed client, with a rigorously secretive agenda,
set an ECPP record in 1997 that has only just recently
been exceeded in public.
Are there other "secret" big proofs, one wonders?