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Within the GIMPS project, there are several different tasks that must be accomplished, in order to achieve the main goals of GIMPS (finding Mersenne primes, ensuring that no Mersenne primes have been missed, and lastly finding factors for Mersenne numbers).

These tasks for the core of the worktypes that Prime95 uses.

List of basic worktypes

  • Trial factoring: Checking for factors of the Mersenne number. A found factor will conclusively prove that the number is composite, which elminates the need to run a primality test.
  • P-1: A second method that finds factors.
  • Lucas-Lehmer test: The primality test. This is the only work type that can prove a number is prime.
  • DC (double check): The same test as the Lucas-Lehmer, but performed on a different machine and with a different offset. Ensures that a prime was not missed by error.
  • ECM: Elliptic curve method factoring, this is used to find factors. Currently this is only being assigned for low numbers that are known to be composite.

List of extended worktypes

These are variations of the above (and appear as listed in the Prime95 menus).

  • Whatever makes the most sense: This lets the PrimeNet server choose what type of assignment the machine will receive.
  • World Record sized number to test: The PrimeNet server will hand out a first time LL test that is larger than the currently known record prime.
  • First time tests: An LL primality test on a number that hasn't previously been tested for primality.
  • Double-check tests: See DC above
  • Trial factoring: See Trial Factoring above.
  • P-1 factoring: See P-1 above.
  • Trial factoring to low limits: PrimeNet assigned LMH work. Shorter duration TF work.
  • ECM on small numbers: Doing ECM factoring on Mersenne numbers with exponents below 1,000,000.
  • ECM on Fermat numbers: Doing ECM factoring on Fermat numbers. (This work type does not contribute toward GIMPS main goals.)
  • 100,000,000 digit numbers to test: Performing L-L primality testing on Mersenne numbers that have at least 100-million decimal digits. A prime number found by this worktype would eligible for the next EFF prize.

Note: Any first time primality test assignment will also include any trial factoring and p-1 factoring that has not yet been completed.

See also