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# Worktype

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 eliminates 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.
• PRP testing: Tests whether a number is likely to be prime or not. This test employs robust error checking which improves the reliability of results, even on flaky hardware. A positive result from this will then be sent to be definitively tested for primality via LL.

## 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 LL test: The PrimeNet server will hand out a first time LL test that is larger than the currently known record prime.
• First time LL tests: An LL primality test on a number that hasn't previously been tested for primality.
• Double-check LL tests: See DC above
• First time PRP tests: A PRP test on a number that hasn’t been tested for primality with either LL or PRP.
• World record sized numbers to PRP test: Similar to World Record sized number to LL test, but uses the PRP test.
• Double-check PRP tests: Double checks a PRP test.
• 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 20,000,000. This is broken up into two categories: ECM for first factors of Mersenne numbers and ECM on Mersenne cofactors.
• 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 LL test (not recommended): 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. This work type is not recommended due to the chance of an error.
• 100,000,000 digit numbers to PRP test: Same as the above, but runs a PRP test.
• First time PRP on Mersenne cofactors: Runs a PRP test on a cofactor of a (relatively) small Mersenne to see if we have probably fully factored a number. If the cofactor is small enough and is probably prime, Primo is then used to produce a primality certificate.
• Double-check PRP on Mersenne cofactors: Double checks a previous PRP test on a cofactor.

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