What exactly is ECM? / How to read the table?

[jmb1982]

I have a question, because I do not complete understand the table given on www.mersenne.org/primenet. How do I have to read it? Did I get it right?:

----------=-----=-- | -----=-----=-----=-----=----- | -----=-----=-----=----- | -----=-----=-----=----- |
Exponent Range | Composite | Status Unproven | Assigned | Available |
Start Count P | F LL-D | LL LLERR NO-LL | ECM P-1 LL LL-D | ECM P-1 LL LL-D |
----------=-----=-- | -----=-----=-----=-----=----- | -----=-----=-----=----- | -----=-----=-----=----- |
Exponent start: obviously... ;-)
Range count: number of possible primes?
P: Number of primes found within the range count?

F: Numbers where has been a factor found while TF'ing?
LL-D: Numbers where has been a factor found while LL-D?
so that P + F + LL-D = Range Count
(or at larger numbers: P+F+LL-D+LL+LLERR+NO-LL = Range count)

So for example, in the first line, there are 3796 Numbers Assigned for ECM and 20706 Available for ECM. Where do these 20706+3796 = 24502 numbers come from? I can't find them in the table...

0 78498 33 | 57747 20718 | 3796 | 20706 |

Thank you... :)

[starrynte]

Originally Posted by jmb1982

Exponent start: obviously... ;-)
Range count: number of possible primes?
P: Number of primes found within the range count?
F: Numbers where has been a factor found while TF'ing?
LL-D: Numbers where has been a factor found while LL-D?

Yes, except LL-D doesn't find a factor, it only proves it composite/prime.

Originally Posted by jmb1982

So for example, in the first line, there are 3796 Numbers Assigned for ECM and 20706 Available for ECM. Where do these 20706+3796 = 24502 numbers come from? I can't find them in the table...

ECM is done on small exponents to find factors. I'm guessing that since some exponents have already been ECM-factored, they are neither assigned nor available. Thus it is not seen in the table.

[Prime95]

Originally Posted by jmb1982

Exponent start: obviously... ;-)
Range count: number of possible primes?

Read it left to right. Actually it is "Exponent Range" referring to all 3 columns. "Start" is "start of the range" your example line represents the
range 0 to 1 million (the start of the range on the next line). "Count" is
the number of prime exponents in the range. "P" is the number of known Mersenne primes in the range.

in the first line, there are 3796 Numbers Assigned for ECM and 20706 Available for ECM. Where do these 20706+3796 = 24502 numbers come from?

People can ECM non-prime exponents. Also, a single exponent can be assigned to several people. For example, there are dozens of ECM assignments active on M1061.

[Mr. P-1]

Originally Posted by jmb1982

Range count: number of possible primes?

The number of prime numbers within the exponent range. These are all tiny and easily enumerated using a sieve. For any prime p within the range, Mp is a "possible" prime only if no factor is known, and no LL test on it has been completed and verified with a doublecheck.

P: Number of primes found within the range count?

For clarity, it is the number of known Mersenne primes whose exponent lies within the range count.

F: Numbers where has been a factor found while TF'ing?

Factored by any method.

LL-D: Numbers where has been a factor found while LL-D?

LL-tested and verified with a doublecheck. No factor known.

[Mr. P-1]

Originally Posted by Prime95

People can ECM non-prime exponents.

They can. They can also ECM prime-exponent Mersenne numbers with known factors.

Also, a single exponent can be assigned to several people..

Also true. But from the numbers, it looks like only unassigned-to-anyone, unfactored, prime-exponent Mersenne numbers are deemed "available".