When found, this was the largest known case of

(January 2005 David Broadhurst announced two 7535-digit CPAP-3, the larger proved in February by François Morain.)

The current CPAP records are at The Largest Known CPAP's.

The titanic records are also at the top twenty Consecutive Primes in Arithmetic Progression in Chris Caldwell's The Prime Pages.

An announcement of this record and the used algorithm is on the Number Theory List.

87

The certificate files are offline after a website move on January 23 2009 so some of the below links are not working.

Torbjörn Alm proved 87

The total running time was around 5000 hours.

Hans Rosenthal originally proved 87

He later proved it again with Primo 2.2.0 beta 4 on an AMD Athlon XP 2400+ cpu running at 2.0 GHz. This certificate is in http://hjem.get2net.dk/carlkruse/certif/cpap7402b.zip (3.6 MB)

The total running time was 3148 hours with more details in http://hjem.get2net.dk/carlkruse/certif/cpap7402b-time.txt

Both certificates have been verified by both Primo and Jim Fougeron's Cert_Val.

They are currently the 2nd and 3rd largest Primo certifications.

Based on experiments with an earlier Primo version, Mike Oakes once estimated the time for phase 1 is typically around proportional to bits^4.86.

There have been other estimates and Marcel Martin has never published an estimate to my knowledge. It is known that running time can vary a lot for candidates of the same size.

Torbjörn Alm kept a log of his Primo certification:

http://hjem.get2net.dk/carlkruse/certif/cpap7402a-primolog.txt (33 kB)

Primo implements the ECPP algorithm. Phase 1 repeatedly reduces the size of a number which must be proven prime to prove the original candidate.

The log has some lines like:

Made by Jens Kruse Andersen, jens.k.a@get2net.dk home

Last updated 12 June 2014