Difference between revisions of "LL test distribution"

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At any given instant, most of [[Great Internet Mersenne Prime Search|GIMPS]]'s LL tests fall roughly into one of 2 categories. As time passes and GIMPS exhausts smaller exponents, both leading edges tend to move upwards, towards larger exponents.
 
At any given instant, most of [[Great Internet Mersenne Prime Search|GIMPS]]'s LL tests fall roughly into one of 2 categories. As time passes and GIMPS exhausts smaller exponents, both leading edges tend to move upwards, towards larger exponents.
  
==Double Checking Leading Edge=={{Last update|2008-09-01}}
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==Double Checking Leading Edge=={{Last update|2020-02-12}}
This refers to the relatively narrow band in which most current double checks are taking place. As of Sept. 2008, most double checks are in the low 20 millions.
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This refers to the relatively narrow band in which most current double checks are taking place. As of Feb. 2020, most double checks are in the 50 million range.
  
 
==First time LL Leading Edge==
 
==First time LL Leading Edge==
This refers to the relatively narrow band in which most current first time [[Lucas-Lehmer test|LL tests]] are taking place. [[Mersenne prime]] discoveries almost always take place in this range. As of Sept. 2008, most first time tests are in the high 30 millions or low 40 millions.
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This refers to the relatively narrow band in which most current first time [[Lucas-Lehmer test|LL tests]] are taking place. [[Mersenne prime]] discoveries almost always take place in this range. As of Feb. 2020, most first time tests are in the 90 million range or low 100 million range.
  
 
Back when first time tests below 10 million digits were plentiful, there was a "10 million digit Leading Edge" as well, which originated at 33.2M and gradually moved upwards. But as first time exponents below 33.2M were gradually exhausted, this edge merged with the First time LL Leading Edge.
 
Back when first time tests below 10 million digits were plentiful, there was a "10 million digit Leading Edge" as well, which originated at 33.2M and gradually moved upwards. But as first time exponents below 33.2M were gradually exhausted, this edge merged with the First time LL Leading Edge.
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A small minority of LL tests are well outside both leading edges.
 
A small minority of LL tests are well outside both leading edges.
  
A few LL tests are well below the double checking leading edge. The typical reason is that the tester is using very slow hardware, causing the test to take years, in which time the double checking leading edge moves past the test. As of Sept. 2008, the smallest ongoing LL test is around 18 million.
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A few LL tests are well below the double checking leading edge. The typical reason is that the tester is using very slow hardware, causing the test to take years, in which time the double checking leading edge moves past the test. As of Feb. 2020, the smallest ongoing LL test is around 49 million.
  
A few LL tests are well above the first time leading edge. This usually happens because the tester is very ambitious; such a strategy actually reduces a user's chances of discovering a new prime because large exponents take longer to test, so that less tests are completed per unit time. As of Sept. 2008, three exponents between 50.1 and 50.2 million have been checked out.
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A few LL tests are well above the first time leading edge. This usually happens because the tester is very ambitious; such a strategy actually reduces a user's chances of discovering a new prime because large exponents take longer to test, so that less tests are completed per unit time. There is an effort for people to test numbers in the 100 million digit range, which is the next digit size that is eligible for a prize. As of Feb. 2020, there are about 2860 tests in the 332M range.
  
As of Sept. 2008, the largest Mersenne number ever LL tested is 2<sup>{{Num|100000007}}</sup>-1, which has {{Num|30103002}} digits. It was first tested by William Christian in 2006 and successfully double-checked the next year. It gave each user 79.417 CPU years (403.0413 GHz-days) of [[PrimeNet]] credit upon completion. However, an even larger LL test is already underway...
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As of Feb. 2020, the largest Mersenne number ever LL tested is 2<sup>{{Num|999999937}}</sup>-1, which has {{Num|301029977}} digits. It was first tested by ramgeis in 2018, but has not been double checked. It gave the user 27583 GHz-days of [[PrimeNet]] credit upon completion. The largest Mersenne number successfully double checked was 2<sup>{{Num|666666667}}</sup>-1, with {{Num|200686664}} digits. It was tested and double checked by LaurV.
 
{{Navbox GIMPS}}
 
{{Navbox GIMPS}}
 
[[Category:Great Internet Mersenne Prime Search]]
 
[[Category:Great Internet Mersenne Prime Search]]

Latest revision as of 21:32, 12 February 2020

The current distribution of LL tests can be viewed at http://www.mersenne.org/primenet

At any given instant, most of GIMPS's LL tests fall roughly into one of 2 categories. As time passes and GIMPS exhausts smaller exponents, both leading edges tend to move upwards, towards larger exponents.

Double Checking Leading Edge

Last update: 2020-02-12

This refers to the relatively narrow band in which most current double checks are taking place. As of Feb. 2020, most double checks are in the 50 million range.

First time LL Leading Edge

This refers to the relatively narrow band in which most current first time LL tests are taking place. Mersenne prime discoveries almost always take place in this range. As of Feb. 2020, most first time tests are in the 90 million range or low 100 million range.

Back when first time tests below 10 million digits were plentiful, there was a "10 million digit Leading Edge" as well, which originated at 33.2M and gradually moved upwards. But as first time exponents below 33.2M were gradually exhausted, this edge merged with the First time LL Leading Edge.

Other LL tests

A small minority of LL tests are well outside both leading edges.

A few LL tests are well below the double checking leading edge. The typical reason is that the tester is using very slow hardware, causing the test to take years, in which time the double checking leading edge moves past the test. As of Feb. 2020, the smallest ongoing LL test is around 49 million.

A few LL tests are well above the first time leading edge. This usually happens because the tester is very ambitious; such a strategy actually reduces a user's chances of discovering a new prime because large exponents take longer to test, so that less tests are completed per unit time. There is an effort for people to test numbers in the 100 million digit range, which is the next digit size that is eligible for a prize. As of Feb. 2020, there are about 2860 tests in the 332M range.

As of Feb. 2020, the largest Mersenne number ever LL tested is 2999,999,937-1, which has 301,029,977 digits. It was first tested by ramgeis in 2018, but has not been double checked. It gave the user 27583 GHz-days of PrimeNet credit upon completion. The largest Mersenne number successfully double checked was 2666,666,667-1, with 200,686,664 digits. It was tested and double checked by LaurV.