mersenneforum.org  

Go Back   mersenneforum.org > Great Internet Mersenne Prime Search > Math

Reply
 
Thread Tools
Old 2007-11-08, 10:05   #1
henryzz
Just call me Henry
 
henryzz's Avatar
 
"David"
Sep 2007
Cambridge (GMT/BST)

10111001011112 Posts
Default Percent chance of being prime

is there a way of working out what percent chance a number has of being prime based on the highest prime below its square root

less than the square of 3 50% of numbers are prime
less than the square of 5 37.5% of numbers are prime

that is what i would like be able to work out without actually knowing the figures
henryzz is offline   Reply With Quote
Old 2007-11-08, 12:08   #2
xilman
Bamboozled!
 
xilman's Avatar
 
"π’‰Ίπ’ŒŒπ’‡·π’†·π’€­"
May 2003
Down not across

101011000011012 Posts
Default

Quote:
Originally Posted by henryzz View Post
is there a way of working out what percent chance a number has of being prime based on the highest prime below its square root

less than the square of 3 50% of numbers are prime
less than the square of 5 37.5% of numbers are prime

that is what i would like be able to work out without actually knowing the figures
Yes, the chance is either 100% or 0%. A number is either prime or not.

Now, what was the question you really meant to ask?

Paul
xilman is offline   Reply With Quote
Old 2007-11-08, 13:16   #3
henryzz
Just call me Henry
 
henryzz's Avatar
 
"David"
Sep 2007
Cambridge (GMT/BST)

5×1,187 Posts
Default

what i meant was:
how can i work out what percentage of numbers are prime between 2 squares of primes
henryzz is offline   Reply With Quote
Old 2007-11-08, 13:31   #4
R.D. Silverman
 
R.D. Silverman's Avatar
 
Nov 2003

11101001001002 Posts
Default

Quote:
Originally Posted by henryzz View Post
what i meant was:
how can i work out what percentage of numbers are prime between 2 squares of primes
Let p1 < p2 be your two primes. The percentage of primes between
p1^2 and p2^2 is trivially [pi(p2^2) - pi(p1^2)]/(p2^2 - p1^2).
pi(N) is the prime counting function.

This is junior high school level math.

WTP?????
R.D. Silverman is offline   Reply With Quote
Old 2007-11-08, 14:11   #5
Fusion_power
 
Fusion_power's Avatar
 
Aug 2003
Snicker, AL

95910 Posts
Default

Just for Paul, we are going to invent a special kind of prime. We'll call it a Schroedinger prime. We never know if it is prime or not until we ask it. Then it tells us either "I'm prime" or else "I'm composite". But until we ask it, it is a Schroedinger prime and nobody knows if it is alive or dead.

Just a little fun on a Thursday morning.

DarJones
Fusion_power is offline   Reply With Quote
Old 2007-11-08, 14:39   #6
Flatlander
I quite division it
 
Flatlander's Avatar
 
"Chris"
Feb 2005
England

31×67 Posts
Default

Quote:
Originally Posted by Fusion_power View Post
Just for Paul, we are going to invent a special kind of prime. We'll call it a Schroedinger prime. We never know if it is prime or not until we ask it. Then it tells us either "I'm prime" or else "I'm composite". But until we ask it, it is a Schroedinger prime and nobody knows if it is alive or dead.

Just a little fun on a Thursday morning.

DarJones
Yes, this is how things work. The wave function collapses when LLR reaches 100%.
Flatlander is offline   Reply With Quote
Old 2007-11-08, 20:01   #7
Spherical Cow
 
Spherical Cow's Avatar
 
Nov 2004

22×33×5 Posts
Default

I respectfully disagree. I think "primeness" is not subject to the spooky whims of quantum mechanics. I believe a number is prime whether it has been looked at (factored) or not, regardless of the speed or acceleration of the observer relative to the prime. While all else in the universe is at the whim Schroedinger's kitty cat (even existence is not determined until an observer observes), primes are absolute. Primosity is more like the speed of light: absolute, and not subject to the philosophical questions of Schroedinger, Heisenberg, or the old "if a tree falls in the forest when no one is around, does it make a sound?"...recently updated to "if a man makes a statement when there is no woman around to hear it, is he still wrong?"

Norm

Last fiddled with by Spherical Cow on 2007-11-08 at 20:03 Reason: Had to change the cat's litter box...
Spherical Cow is offline   Reply With Quote
Old 2007-11-08, 22:55   #8
jasong
 
jasong's Avatar
 
"Jason Goatcher"
Mar 2005

350710 Posts
Default

Can't we at least agree that statistics are useful up until the time the status of the number is determined? For example, a lot of people like to sieve enough numbers in a range to give a 90% chance of finding a prime. And when the Prime95 program is run, the sieving and P-1 are run according to statistical probabilities. Until you actually know the status of the number, it seems idiotic and/or conceited to keep shouting,"It's either 100% prime or 100% composite." Sure, that's true, but how many people in the general public are in a situation where that matters.

Maybe I should start bringing up the idea of primes with factors that have an imaginary component. In my mind, that's just as relevant.
jasong is offline   Reply With Quote
Old 2007-11-09, 12:59   #9
xilman
Bamboozled!
 
xilman's Avatar
 
"π’‰Ίπ’ŒŒπ’‡·π’†·π’€­"
May 2003
Down not across

103×107 Posts
Default

Quote:
Originally Posted by jasong View Post
Maybe I should start bringing up the idea of primes with factors that have an imaginary component. In my mind, that's just as relevant.
Fine by me.

Anyone who doesn't know what we're talking about might find "Gaussian primes" a good starting point.

Paul
xilman is offline   Reply With Quote
Old 2007-11-09, 20:55   #10
Zeta-Flux
 
Zeta-Flux's Avatar
 
May 2003

7·13·17 Posts
Default

henryzz,

As Silverman said, if p and q are primes, with p>q, then the percentage of primes between p^2 and q^2 is

( pi(p^2) - pi(q^2) )/ (p^2 - q^2 )

where pi(x) is the prime counting function. If your values for p and q are small, you can just use this formula in a computer to find the exact value.

When I read your initial question, I thought you were asking for the percentage of the numbers up to p^2 which are prime. This is pi(p^2)/p^2, which is asymptotic to p^2/ (log(p^2) p^2) = 1/(2 log(p)). This last formula will give you a good rough estimate.
Zeta-Flux is offline   Reply With Quote
Old 2007-11-10, 10:04   #11
henryzz
Just call me Henry
 
henryzz's Avatar
 
"David"
Sep 2007
Cambridge (GMT/BST)

10111001011112 Posts
Default

how without counting the primes can i work this out

i want to use this for hopefully having p and q being 100 digit primes
how long do u think ( pi(p^2) - pi(q^2) )/ (p^2 - q^2 ) would take if p and q are 100 digit primes

is there a quick way
henryzz is offline   Reply With Quote
Reply

Thread Tools


Similar Threads
Thread Thread Starter Forum Replies Last Post
DC chance to find Mersenne Prime houding PrimeNet 1 2014-02-24 20:25
Chance of finding new prime number formulas? columbus Information & Answers 49 2013-03-07 22:36
Sandy Bridge CPU Usage only 50 percent dmoran Software 3 2011-06-14 21:21
area by percent of sun in sky Mini-Geek Puzzles 29 2009-03-19 22:22
Why 100 percent???? Jack007 Lounge 19 2002-11-17 01:35

All times are UTC. The time now is 22:56.


Fri Nov 26 22:56:06 UTC 2021 up 126 days, 17:25, 0 users, load averages: 1.25, 1.23, 1.20

Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2021, Jelsoft Enterprises Ltd.

This forum has received and complied with 0 (zero) government requests for information.

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation.
A copy of the license is included in the FAQ.