Math Is Fun Forum

Primenumbers

Member

Registered: 2013-01-22

Posts: 149

More accurate than the Prime Number Theorem.

The primes there are in a certain range can be estimated because there are;
1 No. not factorable by 2 in (2)
There are 2 No.'s not factorable by 2 or 3 in (6)
There are 8 No.'s not factorable by 2 or 3 or 5 in (30)
There are 48 No.'s not factorable by 2 or 3 or 5 or 7 or in (210)
times 48 by (prime -1) to get the next number of no.'s. i.e. =480 no.'s in (2310) not factorable by 2,3,5,7, or 11.....and so on.

So just work out the percentages and apply the correct one to your number x. For example you will not be concerned with No.'s not factorable by 13 if x<13 squared=169. This should be a far more accurate method than the Prime Number Theorem that approximates the number of primes upto x as x/log(x). You will need a computer to do this.

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"Time not important. Only life important." - The Fifth Element 1997

Agnishom

Real Member

From: Riemann Sphere

Registered: 2011-01-29

Posts: 24,996

Website

Re: More accurate than the Prime Number Theorem.

I don't think that is a substitute for the prime number theorem. The prime number theorem is an assymptotic bound. It can be calculated way faster than actually counting the primes

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'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

Primenumbers

Member

Registered: 2013-01-22

Posts: 149

Re: More accurate than the Prime Number Theorem.

Oh, I see. I just thought it was impossible to get an accurate approximate of the number of primes without actually counting them.......... .

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"Time not important. Only life important." - The Fifth Element 1997