mersennekiller

[diep]

They are all primes or just have as a factor 3.

With your farm you could take a gamble and just check just the prime exponents that didn't sieve out and take it to some huge depth. So no brute force search.

My farm not huge enough.

You might win it from Mersenne.

[Batalov]

Originally Posted by diep

They are all primes or just have as a factor 3.

What makes you think that?

[diep]

Originally Posted by Batalov

What makes you think that?

Well it's already a 0.5% formula and if you filter from the exponents all exponents that are not primes themselves, how much do you get left with to check?

0.1% or so?

Paul trying it with pari now - we'll soon know.

edit: and yes you'll miss a few primes by that filter yet if you miss say half of all primes and you reduce input by factor 5 or more, then i bet it's worth it :)

And you do not double check too much - as your machines i bet have ECC :)

edit2: you will get left with 0.045%

[Batalov]

Originally Posted by diep

Well it's already a 0.5% formula and if you filter from the exponents all exponents that are not primes themselves, how much do you get left with to check?

0.1% or so?

edit2: you will get left with 0.045%

What?

[diep]

After sieving you get left with 0.45% - 0.50% of the exponents to check.
From those exponents you remove all composites. Then you get left with 0.045%

It's a mersennekiller.

[Batalov]

No. It is a belief held with strong conviction despite superior evidence to the contrary.

[diep]

You refer to double checking Batalov?

[Batalov]

No

[diep]

Well then you have to keep awake all night and let the primes speak for themselves :)

[VBCurtis]

Originally Posted by diep

After sieving you get left with 0.45% - 0.50% of the exponents to check.
From those exponents you remove all composites. Then you get left with 0.045%

It's a mersennekiller.

Can you explain this again? Sieving is the process of removing known composites, where "known" = "has a small factor". So, what are you doing in the "remove all composites" step, after you have sieved? If you knew a priori which ones were composite, and removed them, you'd be left with a list of primes.... so something seems wrong with the words you have chosen.

Do you mean you check only prime exponents? If so, why? What makes you think prime exponents are more likely to be prime than the rest of the list of exponents that survive a sieve?

[paulunderwood]

Originally Posted by VBCurtis

Can you explain this again? Sieving is the process of removing known composites, where "known" = "has a small factor". So, what are you doing in the "remove all composites" step, after you have sieved? If you knew a priori which ones were composite, and removed them, you'd be left with a list of primes.... so something seems wrong with the words you have chosen.

Do you mean you check only prime exponents? If so, why? What makes you think prime exponents are more likely to be prime than the rest of the list of exponents that survive a sieve?

Yes, Vincent means: check only prime exponents from PG's sieve data. Why? The first two exponents are 127 and 1279. Do you recognise those? Serge's prime had a prime exponent. Of the 5 exponents know to Vincent, 3 are prime. There are about 450 candidates per a domian of 1 million to check.