There are two main types of scripts here:  benchmarks and correctness tests.

The test-* scripts are generally trying to test one part of the module
against another part of the module, an external module, or an external program.
These usually consist of a combination of fixed tests and a long sequence of
testing with random numbers, trying to find things the standard testing might
have missed.


test-factor-yafu.pl

  Tests factorization compared with YAFU (v1.31.1).  No arguments.

test-factor-mpxs.pl

  Tests factorization compared with Math::Factor::XS (v0.26).
  One argument gives the number of random tests to perform.

test-nextprime-yafu.pl

  Tests next_prime() compared with YAFU (v1.31.1).  No arguments.

test-primes-yafu.pl

  Tests primes($a,$b+$interval) compared with YAFU (v1.31.1).  No arguments.
  The interval is currently 8000.

test-holf.pl

  Tests the holf_factor() function vs. the factor() function.  Given enough
  rounds, HOLF (like Fermat) should be able to factor a number.  We keep
  calling it on each non-prime return value until it's done.

test-nthapprox.pl

  Tests the nth_prime approximation and upper/lower bounds vs. known values
  for the nth prime on large values.

test-pcapprox.pl

  Tests the prime_count approximation and upper/lower bounds vs. known values
  for Pi(x) on large values.  Also examines the Schoenfeld and Stoll
  inequalities.

bench-factor-extra.pl

  Benchmarks the various factoring options (prho, pbrent, pminus1, fermat, holf,
  squfof, trial) on random n-digit numbers.  Also gives the percent of the time
  solutions were found with the given number of rounds (256k for SQUFOF, 2000
  for HOLF, and 400 for probabilistic methods).

bench-factor.pl

  Benchmarks factoring random and semiprime n-digit numbers using the factor
  method, and compares vs. Math::Factor::XS (v0.26).  The latter uses a trial
  division algorithm.  MPU 0.05 and later use a threshold of 10M (8 digits)
  to switch between trial division and methods like SQUFOF, Pollard's Rho, and
  HOLF.

bench-factor-semiprime.pl

  Benchmarks factoring semiprimes, and compares with Math::Prime::XS and
  Math::Pari.  Takes two optional arguments: the number of digits (default 15)
  and the benchmark count (default -2, meaning 2 seconds).

bench-is-prime.pl

  Benchmarks is_prime on random n-digit numbers, n from 5 to 10/20.  Compares
  MPU's is_prime and is_prob_prime vs. Math::Prime::XS and optionally
  Math::Primality, Math::Pari, and Math::Prime::FastSieve.  The first two of
  the optional modules use methods more appropriate for big numbers, so are up
  to an order of magnitude slower for 64-bit numbers.  The last module (MPFS)
  is extremely fast, but requires presieving to at least the number to be
  tested, which is great for small numbers, but not for large.
    Also, no additional precalc is done for MPU.  If you really want blazing
  fast is_prime and don't care about the memory and time to sieve, run
  prime_precalc to the limit of your numbers and is_prime will turn into a
  sub-100 microsecond bit array lookup for any number in the range.
    Takes one optional argument of the benchmark count (default -5).

bench-miller-rabin.pl

  Benchmarks the strong miller_rabin test using 7 bases at various digit counts.
  Takes one optional argument of the benchmark count (default -5).

bench-nthprime.pl

  Benchmarks the speed of nth_prime with various digit sizes.

bench-pcapprox.pl

  Benchmarks the speed of prime_count related functions for random n-digit
  numbers (n = 5 to 10/20).  This includes lower bound, lower/upper average,
  the prime_count_approx function, li(x), and R(x).
  Takes one optional argument of the benchmark count (default -5).

bench-primecount.pl

  Benchmarks the speed of prime_count on random n-digit numbers (n = 2 .. 8).
  Takes one optional argument of the benchmark count (default -5).
  I'll note you can easily see the transition from where we're just counting
  existing value to where we have to sieve.  Adding a prime_precalc(10**9)
  line will speed up the 5-,6-,7-, and 8-digit prime_counts greatly.

bench-random-prime.pl

  Benchmarks the speed of random_ndigit_prime for various digits.