CPU @ 100%

[davieddy]

People seem to be over pessimistic on this question.

The ball park error rate of LLests is 2%.

But DCs are performed on exponents half the size, which
means they take 4 times less GHz-Days, and are twice as
likely to be prime.

So by DCing, your chance of finding a MP per year is 16%
of your chance doing first time LLtests: not as dramatic a
difference as is often portrayed.

David

PS and as Christenson has mentioned elsewhere,
6 x miniscule = miniscule ;-)

[cheesehead]

Originally Posted by davieddy

People seem to be over pessimistic on this question.

< snip >

But DCs are <snip > are twice as
likely to be prime.

So by DCing, your chance of finding a MP per year is 16%
of your chance doing first time LLtests:

The most common error in probability calculations is failing to include the effects and consequences of knowledge.

Your calculation seems to assume that the probability of a DC assigned exponent's being that of a Mersenne prime is just as though it were the corresponding probability for first-time tests -- without using any knowledge gained from the first-time tests. That assumption's not valid!

In actuality, GIMPS does not assign DCs for exponents which are already known to be Mersenne primes!

Thus, a correct calculation would have to take into account that GIMPS is deliberately and knowingly _not_ assigning DCs for exponents of known Mersenne primes.

not as dramatic a difference as is often portrayed.

... only because you neglect to account for the effects of prior knowledge!

[davieddy]

I deliberately refrained from including the necessary pedantry.

Given that a first time LLtest is erroneous, (2% say), the probability
of the a DC being prime is doubled while the test time is quartered.

What earthly difference does "already found MPs" make to this
sound and simple conditional probability argument?

David

[cheesehead]

Originally Posted by davieddy

I deliberately refrained from including the necessary pedantry.

... which allowed misinterpretation, because your actual statement was not your intended statement. :-)

What earthly difference does "already found MPs" make to this
sound and simple conditional probability argument?

None, but "this" argument is not the same as the "So by DCing, your chance of finding a MP per year" statement to which I previously replied.

[davieddy]

Originally Posted by cheesehead

... which allowed misinterpretation, because your actual statement was not your intended statement. :-)

None, but "this" argument is not the same as the "So by DCing, your chance of finding a MP per year" statement to which I previously replied.

The statement stands.

[wblipp]

Originally Posted by cheesehead

... only because you neglect to account for the effects of prior knowledge!

I'm skimming, so I may have missed something important.

But didn't David start with the prior knowledge that only 2% of the first tests are faulty, so if all things were equal, you would be 2% as likely to find a prime.

But these tests, if done correctly, are twice as likely to be prime, so in the same number of tests you are 4% as likely to find a prime.

But the tests are four times faster, so in the same time you are 16% as likely to find a prime.

I don't see what additional prior knowledge would be relevant to the calculation. In particular, knowledge of known Mersenne Primes is not knowledge about faulty tests - those tests are known to be correct, so not relevant to this analysis.

William

[Brian-E]

Originally Posted by cheesehead

Thus, a correct calculation would have to take into account that GIMPS is deliberately and knowingly _not_ assigning DCs for exponents of known Mersenne primes.

My own understanding, and it is likely to be faulty since I have studied no probability theory in more than 25 years, is that the above statement is quite correct in that it identifies a biasing factor. However surely the bias in this case is so tiny (there are so few identified Mersenne Primes) that it will have no effect on the very rough 16% estimate which David arrives at.

[davieddy]

Originally Posted by Brian-E

the very rough 16% estimate which David arrives at.

THX Brian (and William).

Not all that rough though. OK someone can work out a more accurate
current "error rate" (E%) by the DCs whose residues don't match the
first LL, but I made it clear that "2%" was a ball park guess at E%.

Doubling the exponent increases the GHz-Days by slightly more than 4 times.
The probability of being prime is complicated by "how far TFed" etc, but it involves 1/exponent.

If I said "8E%" instead of "16%" I would not be too far out.

David

[LiquidNitrogen]

Blah blah blah blah blah, you guys should run for office.

[davieddy]

Originally Posted by cheesehead

The most common error in probability calculations is failing to include the effects and consequences of knowledge.

Your calculation seems to assume that the probability of a DC assigned exponent's being that of a Mersenne prime is just as though it were the corresponding probability for first-time tests -- without using any knowledge gained from the first-time tests. That assumption's not valid!

In actuality, GIMPS does not assign DCs for exponents which are already known to be Mersenne primes!

Thus, a correct calculation would have to take into account that GIMPS is deliberately and knowingly _not_ assigning DCs for exponents of known Mersenne primes.

... only because you neglect to account for the effects of prior knowledge!

I think all your qualms boil down to obtaining an unbiassed estimate
of the probability of the non-zero residue of an unverified LL being wrong.

No doubt a determined quibbler will find this too simple,
but I would take a suitable* large sample of "verified composite via
two matching residues", and find the % where the first test proved
to be wrong.

This totally bypasses your "known prime" "difficulty".

David

* I am "covering my back" this time by allowing
you to decide what "suitable" means!

[davieddy]

Originally Posted by LiquidNitrogen

Blah blah blah blah blah, you guys should run for office.

More than you needed to know ATM?

"Us guys" (comparative veterans) still enjoy "getting it straight".


David