GIMPS type of work

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You have the choice of 6 main types of work units (WU) you can do for the project. The client can also do other types of work as well, but they are outside the scope of this page (for more information see the readme.txt that comes with the client). The different types are listed in the order that they are performed on an exponent.

Factoring of a prime number (exponent) candidate

Trial factoring is a pre check of a candidate exponent. These work units take the least time and are given out by the server according to your CPU speed. They may go through several iterations of bit length before clearing and getting sent to a fast machine for the more intensive Lucas-Lehmer testing. Although CPU’s can be used for this task, a GPU is much faster for doing this when mfaktc/mfakto are used. There is no chance of finding a prime through factoring.

Lone Mersenne Hunters is a project trial factoring candidates outside the normal range of exponents.

P-1 factoring

This is a different type of factoring than trial factoring. Unlike TF, the P-1 factorization method is not done a single bit level at a time. Rather bounds are used. The more memory available the greater the chance of finding a factor. P-1 factoring takes longer per single unit than TF, but the chance of finding a factor (especially large factors) are greater (per each WU).

ECM factoring

This is also a different type of factoring than trial factoring. This uses the Elliptic curve method, and work units of this type are typically distributed 1-3 curves at a time from PrimeNet (one can change the number of curves by modifying Worktodo.txt). This is run on smaller exponents (<20 million) in the hopes of fully factoring them.

(First time) Lucas Lehmer (LL) testing on a prime candidate

Lucas-Lehmer is the actual primality test; the chance of finding a prime candidate is currently somewhere on the order of one in several hundred thousand. Pre factoring is designed to ensure that no time is spent on lengthly LL work when a relatively small factor is present. There are several variations of this currently available:

  • Standard (take the next exponent the server hands out, takes 1 to 2 weeks on typical hardware[1])
  • World Record (request an exponent that will yield a number larger than the current record. If all the first time tests are larger than the biggest known prime, then this is the same as standard)
  • 100 million digit (request an exponent that will yield a number with at least 100 million digits, these will take around 2 weeks on a Radeon VII, or several weeks on high end consumer hardware [2]). The 100 million digit level is the level that could win the next Electronic Frontier Foundation prize.

Double checking a prime candidate

Double checking is done to work units which have cleared one round of Lucas-Lehmer testing. This verifies that the LL test has concluded correctly and ensures that the computer that performed the first LL test performed to specifications. These are small to medium units, and they typically take a few days to run on typical hardware. Basically this is a Lucas-Lehmer test, but the exponent size is smaller than for the current first time primality test range because a few years typically pass between the first LL test of an exponent and it's doublecheck, by which time GIMPS has moved on to larger exponents.

PRP testing

PRP testing can also be run on prime canadidates. The PRP test used in Prime95 uses a special type of error checking developed by Robert Gerbicz which greatly improves the reliability of results. This test does not, however, definitively determine if a candidate is prime if a positive result occurs. If such a thing happens, then the candidate will undergo a LL test to conclusively test its primality. Like the LL tests, PRP tests come in the same flavors (standard, world record, 100 million digit tests, and DC). There is also the option to test Mersenne cofactors to see if we have probably fully factored a number [3].

See also

References

  1. By typical, I am referring to a quad core Intel with AVX2 instructions (Haswell or newer) or the equivalent AMD Ryzen CPU
  2. The Hardware Jest Thread on Mersenneforum
  3. See the following thread: Mersenne number factored (disbelievers are fools)