Is the set of prime number finite? if?

  • Thread starter Shad0w7
  • Start date
  • #1
1
0
Let's say I have this statement. {a^p | p is prime and p < N}

a is considered a string so

so a^2 = aa, a^3 = aaa and so on....

anyway, in this case, since it says that p< N, then is mean that p will be finite right??
 

Answers and Replies

  • #2
HallsofIvy
Science Advisor
Homework Helper
41,847
966
First, let me point out that the answer to the question asked in the title, "is the set of prime numbers finite", is "NO"- the set of all prime numbers is infinite- that proof was given by Euclid, thousands of years ago.

But the answer to the question asked in your text, "Is the set of all numbers of the form [itex]a^p[/itex] where a is a given number and p is a prime number less than N finite" is "YES". In fact, the "prime" part is irrelevant. If a is a fixed number, then the set of all [itex]a^n[/itex], where n is any positive integer less than N, is finite.
 

Related Threads on Is the set of prime number finite? if?

  • Last Post
2
Replies
40
Views
5K
  • Last Post
Replies
19
Views
2K
  • Last Post
Replies
15
Views
7K
  • Last Post
Replies
8
Views
3K
  • Last Post
Replies
12
Views
2K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
5
Views
2K
  • Last Post
Replies
3
Views
1K
Replies
10
Views
18K
Top