Prime Numbers Not Random?

B

Ben-CS

Guest
The sequence of primes is entirely deterministic. There are even nth prime formulae; however, the formulae are of exponential complexity...or worse.

Addendum: Oh, there's a link. The site explains how the sucession of primes is not so apparantly random after all.
 
Last edited by a moderator:

Hurkyl

Staff Emeritus
Science Advisor
Gold Member
14,829
14
It gets better than that.

There exist polynomials p(n) (n integer) that only take on prime or negative values. Even bettern there exist polynomials p(n) that can be every prime number and some negative values, but nothing else!

There even exists a formula for the n-th prime number! (I've only heard this referenced though, I have never actually seen it)

Hurkyl
 
C

climbhi

Guest
Originally posted by Hurkyl
There even exists a formula for the n-th prime number! (I've only heard this referenced though, I have never actually seen it)

Hurkyl
What if this is true, why are they still searching for big prime numbers with computers and stuff. Why don't they just plug 100,000,000,000,000,000,000,000,000,000,001 in for the n and get a massive prime number. I really have to doubt about this part.

What are the functions you were refering to that take on all prime numbers and some negative numbers. Those sound kind of interesting.
 
B

Ben-CS

Guest
Why don't they just plug 100,000,000,000,000,000,000,000,000,000,001 in for the n and get a massive prime number?
Exponential Complexity:

If T(f; n) is the time it takes to calculate f(n), the T(f; n + 1) is approximately T(f; n) times some constant k > 1. Attempting to calulate the 100,000,000,000,000,000,000,000,000,000,001st prime would probably require more eons than there are Angstroms in a lightyear.
 
3,036
3
Hurkyl
There even exists a formula for the n-th prime number! (I've only heard this referenced though, I have never actually seen it)
Urban Legend?
 

The Physics Forums Way

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving
Top