The Jargon File (version 4.4.7, 29 Dec 2003):

pseudoprime
 n.

    A backgammon prime (six consecutive occupied points) with one point
    missing. This term is an esoteric pun derived from number theory: a number
    that passes a certain kind of ?primality test? may be called a pseudoprime
    (all primes pass any such test, but so do some composite numbers), and any
    number that passes several is, in some sense, almost certainly prime. The
    hacker backgammon usage stems from the idea that a pseudoprime is almost as
    good as a prime: it will do the same job unless you are unlucky.


The Free On-line Dictionary of Computing (30 December 2018):

pseudoprime

   A backgammon prime (six consecutive occupied points) with one
   point missing.  This term is an esoteric pun derived from a
   mathematical method that, rather than determining precisely
   whether a number is prime (has no divisors), uses a
   statistical technique to decide whether the number is
   "probably" prime.  A number that passes this test is called a
   pseudoprime.  The hacker backgammon usage stems from the idea
   that a pseudoprime is almost as good as a prime: it does the
   job of a prime until proven otherwise, and that probably won't
   happen.

   [Jargon File]