Introduction
This page shows the largest known case of k primes in AP (arithmetic progression) for each k, with a record history. It also shows the minimal or smallest known difference, start and end in an AP − k, with record histories. Finally it shows all known AP24 until an AP26 was found, and all known AP25. Record histories begin with the record when the page opened in January 2005.
An AP − k is k primes of the form p + d • n for some d (the difference between the primes) and k consecutive values of n. Technically any 2 primes form an AP2 but this page is only about AP3 and longer.
Some sources say PAP − k instead of AP − k to signal it is primes in AP.
The Largest Known CPAP's is a different page with records for consecutive primes in AP.

Dirichlet's Theorem on Primes in Arithmetic Progressions says there are always infinitely many primes of the form c + d • n, when c and d are relatively prime − and consecutive n's are not demanded.
Ben Green & Terence Tao presented a proof in 2004 that The primes contain arbitrarily long arithmetic progressions. It shows existence of AP's but does not help in finding them.

k# (called k primorial) is the product of all primes ≤ k, e.g. 10# = 2 • 3 • 5 • 7.
2# = 2, 3# = 6, 5# =30, 7# = 210, 11# = 2310, 13# = 30030, 17# = 510510, 19# = 9699690, 23# = 223092870.
Unless k is prime and starts an AP − k, the difference in an AP − k is always a multiple of k# to avoid factors ≤ k. Expressions with larger primorials are often used in AP searches to avoid more small factors. Most large AP's are found roughly like this:
First compute a large set of primes a • q# + 1 for fixed q. Then find AP's among the a's.
This gives an AP formula like (4941928071 + 176836494 • n) • 2411# + 1, for n=0..7
It can be written on the form p + d • n: (4941928071 • 2411# + 1) + (176836494 • 2411#) • n

Submissions
I would like to hear of all new records.
Please mail any you find or know about to pzktupel@pzktupel.de.
All primes must be proven, i.e. prp's (probable primes) are not allowed.
The largest prime in an AP determines which AP is judged largest, so an AP3 record could start at 3.
An AP − k is also considered to be an AP − (k - 1), so it can hold the record for different k's.

n's not starting at 0 indicates the end of a longer AP. The listed number of digits is for the largest prime in all tables. A year link is to an announcement. The k value links to the record history.

Credited programs and projects
See Software Collection

Links
From Chris Caldwell's The Prime Pages:
The Top Twenty: Arithmetic Progressions of Primes (only primes with at least 1000 digits)
The Prime Glossary: arithmetic sequence
The Prime Database: Search on Arithmetic
Dirichlet's Theorem on Primes in Arithmetic Progressions