Call me lazy but...
 

ASSUMING we can expect 1.78 Mersenne primes between
exponents x and 2x, what ratio r of exponents gives us the "half life"
(0.5 probabiliiy of no primes between x and rx)?

I miss Mally's prolific old chestnuts.

David

I think there are large assumptions (on top of the ones you've already made) that are necessary before this is solvable. I'm pretty sure that once those assumptions are made, the result will have nothing to do with Mersenne primes

OK forget the sodding Mersenne primes, but I'm pretty sure
there are some people here (Blipp being one) who can interpret/rigorize the
question and supply an answer.

PS I remember your proclaimed disdain for "Applied Math"

David

[QUOTE=davieddy;191323]OK forget the sodding Mersenne primes, but I'm pretty sure
there are some people here (Blipp being one) who can interpret/rigorize the
question and supply an answer.

PS I remember your proclaimed disdain for "Applied Math"

David[/QUOTE]

There's no need to get pissy. You just need to figure out what you're asking.

Expected values don't tell us anything about the distribution, so we need to assume a distribution before we can even attempt the problem.

It's possible that assuming the expected value is 1.78 across all intervals forces a single distribution, but I think you'd need to assume your distribution was continuous.

And what the hell does applied math have to do with this?

Hmm, thinking on it for more than 15 seconds, I might have to retract my statement.

I think r = 1.21495... is what you're looking for.

This is assuming that the expected number of mersenne primes in the interval (x,rx) is log[sub]2[/sub](2[sup]n[/sup])*1.78 (i.e. in the interval (x,4x), we expect to find 3.56 mersenne primes)

OK I'll check it out in the morning when I'm sober.
(and you will still be ugly... (Churchill))

Meantime I'm searching for Flouran's description of me as "great".

I wanted to say "Some are born great, some achieve greatness,
and others have it thrusted upon them"

[quote=Orgasmic Troll;191328]I think r = 1.21495... is what you're looking for.

This is assuming that the expected number of mersenne primes in the interval (x,rx) is log[sub]2[/sub](2[sup]n[/sup])*1.78 (i.e. in the interval (x,4x), we expect to find 3.56 mersenne primes)[/quote]
I assume you meant e.g. and not i.e.

[QUOTE=davieddy;191332]I assume you meant e.g. and not i.e.[/QUOTE]

no, I think "that is" fits in there just as well.

[quote=Orgasmic Troll;191328]I think r = 1.21495... is what you're looking for.

This is assuming that the expected number of mersenne primes in the interval (x,rx) is log[sub]2[/sub](2[sup]n[/sup])*1.78 (i.e. in the interval (x,4x), we expect to find 3.56 mersenne primes)[/quote]
We are extracting more mileage out of this thread than I anticipated.
Does n=r?

More to come.

David

Fawlty Towers
 

Sybil is wizard on "Mastermind" - speciality topic:
The Bleedin' Obvious.

Can you get that pigeon out of the water tank
please. The hotel inspectors will be round in a minute.
Manuel: "Que?"
This isn't a proposition from Wittgenstein