EFF claim(s)

[Wacky]

Originally Posted by Peter Nelson

I conjecture that the total number of dogs is in fact prime.

Statistically, the odds are against you. Since the population is large and the lifespan of any individual is bounded, the "total number of dogs" is constantly changing. Therefore, it can be demonstrated that, your conjecture is false more often than it is true.

[Fusion_power]

Maybe its time to let sleeping dogs lie.

Xilman, Would you care to engage in a discourse where I propound that the universe is finite and you that it is infinite? I think I could make a good evidential arguement that the universe had an origin (Big Bang) and that it has expanded at a somewhat irrational rate. Since it has both origin and expansion, it must be finite.

Bearnol,

Your basic conclusion is seriously flawed at the point where you stipulate that an infinity of primes necessitates an infinity of Mp's.

[xilman]

Originally Posted by Fusion_power

Xilman, Would you care to engage in a discourse where I propound that the universe is finite and you that it is infinite? I think I could make a good evidential arguement that the universe had an origin (Big Bang) and that it has expanded at a somewhat irrational rate. Since it has both origin and expansion, it must be finite.

Not so. There is nothing in the Einstein field equations which requires an open universe not to contain a singularity at a finite proper time in the past for all observers. Hawking in the mid-sixties showed that all physically realistic cosmologies governed by general relativity must contain a singularity though, of course, this does not in itself prove that they must contain a big bang.

Of course, if G-R is seriously wrong, all bets are off.

Paul

[bearnol]

Originally Posted by jinydu

The problem here is that infinity is not a number. There is no point at which the smallest possible factor becomes "larger than infinity".

I could use the same reasoning to "prove" that

n! + 1

is prime infinitely often.

Well done jinydu!
I do just this (also) on my pages...
J

[bearnol]

Originally Posted by Peter Nelson

If your "proof" showed mersenne primes were indeed infinite, it would be a trivial application of this to show there must exist just one more (at least).

(thanks again for your post, Peter)
It would be, and is, a corollary.
J

[Orgasmic Troll]

</speechless>

[bearnol]

Originally Posted by Peter Nelson

I conjecture that the total number of dogs is in fact prime.

Actually I disagree with this.
Since the total number of dogs in the universe is very large (leaving aside arguments as to whether or not it is/are infinite), then the exact number is far more likely, probabilistically, to be composite.
J

[Peter Nelson]

Originally Posted by bearnol

Actually I disagree with this.
Since the total number of dogs in the universe is very large (leaving aside arguments as to whether or not it is/are infinite), then the exact number is far more likely, probabilistically, to be composite.
J

Wacky and Bearnol, you put forward quite a compelling argument.

In fact I suspected these reasons when posting (somewhat humourously).

However it would be NICE if it was prime.

Wacky stated that the number of dogs is "constantly" changing. More precisely I imagine every few seconds or minutes (not uniformly) one or more dogs are born and one or more dogs die. Therefore the change in dog population will take steps up and down sporadically rather than changing constantly.

Also if (and this would require empirical evidence) the number of dogs born per litter was always ODD (probably untrue), it might be slightly more probable that the number of dogs globally was prime than if dogs/litter was always even.

I agree that it is more likely that for the majority of the time the dog population is composite, however, I believe that there ARE times when it IS prime. You have not shown that the number of dogs CANNOT be prime sometimes, albeit fleetingly. The larger the population of dogs, the less proportion of time that the number of dogs is prime (based on the prime distribution function).

My revised conjecture is that at least once per day every day the number of dogs worldwide IS prime. I believe this is reasonable because the population of dogs is finite.

[Wacky]

Originally Posted by Peter Nelson

My revised conjecture is that at least once per day every day the number of dogs worldwide IS prime. I believe this is reasonable because the population of dogs is finite.

THat would entirel depend on the rate of change in the population. It is known that there are at least some large intervals where there are no primes. If the interval is sufficiently large in comparison to the rate of change in the population, it might take several days for the population to traverse the interval. (That assumes an ever increasing population) If the population is not growing, but simply oscillating about some nominal value, it might never be prime.

[Orgasmic Troll]

are we counting wolves? dingos? coyotes? jackals?

[Peter Nelson]

No I think we should concern ourselves with DOGs only.

Based on observation, I believe the population of dogs to be less than humans.

Estimate 1 billion versus 7ish billion humans.

There ARE large ranges of numbers with no primes. However these gaps are bigger the higher numbers we are looking at.

Numbers up to 1 billion are relatively small and I don't think (I have the data but not handy) that the largest consecutive gap between primes is greater than my estimate of the daily variance in the dog population (assuming some equilibrium of dog numbers). eg due to seasonal variation. Do more dogs die in cold winters?

I leave as a trivial exercise to the reader to state the largest gap between primes for all positive integers up to a billion. You can obtain all the primes up to a billion easily from the links on Chris Caldwell's prime pages.

I estimate that the dog population will change each day on average every 1 second (birth or death). Therefore there are 60x60x24=86400 time points at which the population MIGHT be prime (although not all these will be distinct quantities, some duplicates). Given this it probably for at least one data point exceeds the probability that a number of size circa 1 billion is prime (prime distribution function).