## RE: [PrimeNumbers] Are Big Numbers More Likely To Be Prime?

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• ... increases as A increases. QED. Alan pointed out the Prime Number Theorem, which is truly important, but also consider common sense: past 2, half of the
Message 1 of 4 , May 23, 2010
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> This is tantamount to saying that the probability that A is prime
increases as A increases. QED.

Alan pointed out the Prime Number Theorem, which is truly important, but
also consider common sense: past 2, half of the numbers composites
divisible by 2. Past 3, half of those remaining numbers are divisible
3, past 5, 1/5 are divisible by 5... obviously the density is going down
(on the average).

Good luck!
• ... So far okay... ... ... but why exactly would this ratio describe the probability of a number being a prime? Peter
Message 2 of 4 , May 23, 2010
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> Let A be a natural number. Let S be the set of all prime numbers such
> that any element of S is less than the step function of the square root
> of A.

So far okay...

> Define the probability that A is a prime number as the quotient (A-S)/A.

... but why exactly would this ratio describe the probability of a number
being a prime?

Peter
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