Is it true that any rule regarding prime numbers eventually fails?

  • Thread starter goldust
  • Start date
  • #1
89
1
Other than the fact that prime numbers are infinite?
 

Answers and Replies

  • #2
13,173
7,074
By rule, you mean one that predicts primes then yes they all fail.
 
  • #3
89
1
By rule, you mean one that predicts primes then yes they all fail.

Not just prediction of prime numbers, but any regularity that humans can comprehend. The regularity must be directly operated on primes rather than on another set of numbers, such as the statement that every even number is the sum of two primes, or every even number is the sum of a prime and a semi prime. Also, the regularity can't be probabilistic as in the Prime Number Theorem.
 
Last edited:
  • #4
160
21
No, it is not true. How could it be?

This page has many examples of formulas that generate all the primes (and only the primes).
 
  • #5
89
1
No, it is not true. How could it be?

This page has many examples of formulas that generate all the primes (and only the primes).

Do any of them take prime numbers as inputs? :confused:
 
  • #6
160
21
I don't quite understand your question -- are you asking for something like a formula that takes a number as input, and returns 1 if it is prime and 0 if it is non-prime?

If so, take a look at Wilson's Theorem (or at the first formula on the page I just linked to).
 
  • #7
89
1
I don't quite understand your question -- are you asking for something like a formula that takes a number as input, and returns 1 if it is prime and 0 if it is non-prime?

If so, take a look at Wilson's Theorem (or at the first formula on the page I just linked to).

Wilson's formula is very interesting. :biggrin: Thanks for the info.
 
Last edited:

Related Threads on Is it true that any rule regarding prime numbers eventually fails?

Replies
7
Views
743
  • Last Post
Replies
1
Views
759
  • Last Post
Replies
6
Views
2K
C
  • Last Post
Replies
8
Views
1K
  • Last Post
Replies
12
Views
4K
Replies
8
Views
3K
  • Last Post
Replies
20
Views
3K
Replies
2
Views
2K
Replies
12
Views
2K
Top