What do the different types of work each mean?

[jrafanelli]

I am a math teacher and am pretty computer savvy, but not sure the exact definition of the types of work. I would love to find the next prime number or the biggest one, but what jobs would that be? :) Thanks

[Uncwilly]

Well, if you want to find the next 'biggest known prime', you should set your system for "World record sized numbers to test". This will get from the server exponents that are larger than the most recent largest known. (Practically of late, this has also meant the same as "First time tests", but not at the moment.)

If you want to just look for any prime (size being irrelevant), choose "First time tests".

If you want faster testing, but with a lower chance of finding a prime choose "Double-check tests". These are numbers that have been tested already, but need a run on a different machine to check that there were no errors in the original test. These are smaller numbers and thus run faster.

If you want to go for the big boy, choose "100,000,000 digit numbers to test". This is the next prime size that will win the EFF award. It will be both world record size and a first time test. It will also take longer to test and thus be prone to more problems. I don't recall the time to run with the current best consumer level hardware, but it is over a month per exponent.

[bgbeuning]

Here are all the work types from the prime95 source code.

Most people use work type 0. It checks how fast your machine is
and picks the best work for it. A newer machine will get some double
check (type 101) jobs to test out your hardware, and when it passes
then move up to type 100 jobs.

All the factoring methods help save work by eliminating exponents
from further consideration.

ECM is elliptic curve method of factoring.
P-1 is Pollard's rho method of factoring.
PRP stands for probable prime.

There is a cash prize for finding a 100 million digit prime
and some of the work types are for that.
Read the prime95 license agreement, you are agreeing
to split any prizes with the GIMPS project leaders.
Which is very fair.

/* Valid work_preference values */
#define PRIMENET_WP_WHATEVER 0 /* Whatever makes most sense */
#define PRIMENET_WP_FACTOR_LMH 1 /* Factor big numbers to low limits */
#define PRIMENET_WP_FACTOR 2 /* Trial factoring */
#define PRIMENET_WP_PMINUS1 3 /* P-1 of small Mersennes --- not supported */
#define PRIMENET_WP_PFACTOR 4 /* P-1 of large Mersennes */
#define PRIMENET_WP_ECM_SMALL 5 /* ECM of small Mersennes looking for first factors */
#define PRIMENET_WP_ECM_FERMAT 6 /* ECM of Fermat numbers */
#define PRIMENET_WP_ECM_CUNNINGHAM 7 /* ECM of Cunningham numbers --- not supported */
#define PRIMENET_WP_ECM_COFACTOR 8 /* ECM of Mersenne cofactors */
#define PRIMENET_WP_LL_FIRST 100 /* LL first time tests */
#define PRIMENET_WP_LL_DBLCHK 101 /* LL double checks */
#define PRIMENET_WP_LL_WORLD_RECORD 102 /* LL test of world record Mersenne */
#define PRIMENET_WP_LL_100M 104 /* LL 100 million digit */
#define PRIMENET_WP_PRP_FIRST 150 /* PRP test of big Mersennes */
#define PRIMENET_WP_PRP_DBLCHK 151 /* PRP double checks */
#define PRIMENET_WP_PRP_WORLD_RECORD 152 /* PRP test of world record Mersennes */
#define PRIMENET_WP_PRP_100M 153 /* PRP test of 100M digit Mersennes */
#define PRIMENET_WP_PRP_COFACTOR 160 /* PRP test of Mersenne cofactors */
#define PRIMENET_WP_PRP_COFACTOR_DBLCHK 161 /* PRP double check of Mersenne cofactors */

[heliosh]

There is an entry in the Mersenne Wiki about the different Worktypes:

http://www.mersennewiki.org/index.php/Worktype

One thing that is missing is ECM vs. ECM-CF. I assume ECM is for Mersenne-numbers which don't have a known factor yet and ECM-CF for Mersenne-numbers with one known factor but unknown other factors.
Thus ECM more likely for bigger Mersenne-numbers and ECM-CF more likely for smaller Mersenne-numbers. Is that correct?

[JordanRom]

Originally Posted by Uncwilly

Well, if you want to find the next 'biggest known prime', you should set your system for "World record sized numbers to test". This will get from the server exponents that are larger than the most recent largest known. (Practically of late, this has also meant the same as "First time tests", but not at the moment.)

If you want to just look for any prime (size being irrelevant), choose "First time tests".

If you want faster testing, but with a lower chance of finding a prime choose "Double-check tests". These are numbers that have been tested already, but need a run on a different machine to check that there were no errors in the original test. These are smaller numbers and thus run faster.

If you want to go for the big boy, choose "100,000,000 digit numbers to test". This is the next prime size that will win the EFF award. It will be both world record size and a first time test. It will also take longer to test and thus be prone to more problems. I don't recall the time to run with the current best consumer level hardware, but it is over a month per exponent.

Hi,

New to GIMPS. It looks like there are more options now in v29 and this is still kind of confusing on how to find the next / biggest Mersenne Prime...

So for instance what is the correct "100,000,000 digit numbers to test" PRP or LL?

Thanks for any help!

[Uncwilly]

Originally Posted by JordanRom

New to GIMPS. It looks like there are more options now in v29 and this is still kind of confusing on how to find the next / biggest Mersenne Prime...

So for instance what is the correct "100,000,000 digit numbers to test" PRP or LL?

PRP is a different method of checking. It has some advantages and some disadvantages. Either is ok to select. (Double checks on either type of test should be of the same type.)

Selecting "World Record" will always select a test on a number larger than the largest known prime. At the moment "First time" is also in this range.

Double checks may never find a new prime. And almost certainly it won't be a world record.

ECM is a type of factoring and like all of the factoring methods can't prove a number is prime.
Trial factoring can find factors and thus prove that a number is -not- prime.
P-1 is another factoring method.
Co-factors are what is left after a factor is found. Testing these will never find a new M Prime. Factoring them is for those that want a complete set of factors for a number. (This is part of what is done in GIMPS as well as finding new records.)

[ATH]

Originally Posted by JordanRom

So for instance what is the correct "100,000,000 digit numbers to test" PRP or LL?

You should always use PRP test for very large exponents since it has error checking along the way.

If you are using a Xeon with ECC RAM it does not matter as much, but PRP tests would still be safer.

[JordanRom]

Thank you for the informative answers everyone!

Cheers,
Jordan

[Xyzzy]

Originally Posted by Uncwilly

PRP is a different method of checking. It has some advantages and some disadvantages.

What disadvantages does it have?

[ATH]

If a positive test is found 2 more LL tests are needed to double check. But not much of a disadvantage, since 4+ different double checks are usually done anyway.

[storm5510]

Originally Posted by Xyzzy

What disadvantages does it have?

Disadvantage: It takes a long time to do a PRP on a large exponent. Sometimes longer than LL, in my experience.