## Answer

###### Wiki User

###### 06/15/2010

Yes. To prove this, we must first assume the answer to be no. If there are a finite number of primes, there must be a largest prime. We'll call this prime number n. n! is n*(n-1)*(n-2)*...*3*2*1. n!, therefore, is divisible by all numbers smaller than or equal to n. It follows, then that n!+1 is divisible by none of them, except for 1. There are two possibilities: n!+1 is divisible by prime numbers between n and n!, or it is itself prime. Either way, we have proved that there are prime numbers greater than n, contradicting our initial assumption that primes are finite, proving that the number of primes is infinite.

## Related Questions

###### Asked in Composite Numbers

### Is there an infinite amount of prime and composite numbers?

Because there are an infinite number of numbers, it would stand
to reason that there are an infinite number of prime and composite
numbers.
...

Read More

###### Asked in Factoring and Multiples, Prime Numbers

### What number has five different prime factors?

Since there are an infinite number of prime numbers, there are
infinite numbers with any given number of prime factors.
...

Read More

###### Asked in Prime Numbers

### Can anyone name all the none prime numbers?

No, there are an infinite amount of non-prime numbers just as
there are an infinite number of prime numbers.
...

Read More

###### Asked in Prime Numbers, Numbers

### What is the number of prime numbers?

It is impossible to know the number of prime numbers because
there is an infinite number of them.
...

Read More

###### Asked in Math and Arithmetic, Prime Numbers, Numbers

### Who many prime numbers begin with 9?

Infinity. There's an infinite number of place values, so you can
create an infinite number of numbers that start with nine. Some of
these will be prime, and since there is an infinite number of
numbers starting with nine, there is an infinite number of prime
numbers that start with 9 as well.
...

Read More

###### Asked in Tablets and Handheld Computers, Prime Numbers

### What is the largest prime number in 9 bit register?

Well, there is an infinite number of numbers, so technically,
there is an infinite amount of prime numbers.
...

Read More

###### Asked in Prime Numbers, Numbers

### What are the 25 prime numbers?

There are more than 25 prime numbers; there are an infinite
number of prime numbers.
...

Read More

###### Asked in Prime Numbers

### How man prime number exist in mathematics?

There are an infinite number of prime numbers.

Read More

###### Asked in Math and Arithmetic, Prime Numbers

### What are all the prime numbers 500 and up?

There is an infinite number of prime numbers after 500!

Read More

###### Asked in Prime Numbers

### Are there any prime numbers over 100100?

Yes - there are an infinite number of prime numbers. The first
prime number after 100100 is 100103.
...

Read More

###### Asked in Prime Numbers, Biggest, Strongest, Fastest and Other Extremes

### What is the biggest known prime number?

numbers are infinite. There is no end of numbers

Read More

###### Asked in Prime Numbers

### What are prime numbers greater than 100?

There is an infinite number of prime numbers. It is not possible
to list them.
...

Read More

###### Asked in Prime Numbers

### What are all of the highers prime numbers?

It is impossible to list the infinite number of higher prime
numbers.

Read More

###### Asked in Prime Numbers, Numbers

### What are the prime number after 200?

The prime numbers after 200 are infinite. The next prime number
after 200 is 211.
...

Read More

###### Asked in Math and Arithmetic, Numbers

### Rational numbers between 3 and 5?

There are infinitely many of them.
Some of them are given by:
All numbers of the form 3n+1/n for n ∈ the prime numbers are
rational numbers between 3 & 4, and as there are an infinite
number of prime numbers, there are an infinite number of
these.
All numbers of the form 4n+1/n for n ∈ the prime numbers are
rational numbers between 4 & 5, and as there are an infinite
number of prime numbers, there are an infinite number of
these.
There...

Read More

###### Asked in Prime Numbers, Composite Numbers

### What are all of the composite numbers and all of the prime numbers?

It is impossible to list the infinite number of prime numbers
and composite numbers.
...

Read More

###### Asked in Prime Numbers, Numbers

### What is the lasrgest known prime number?

Impossible to know; prime numbers are infinite.

Read More

###### Asked in Prime Numbers

### Why can a prime number not be abundant?

Prime numbers are abundant, in fact there is an infinite about
of prime numbers. There is just and infinitely greater amount of
non-prime numbers.
...

Read More

###### Asked in Prime Numbers

### What are the last 2 prime numbers?

There cannot be the last two prime numbers because there are an
infinite number of them.
...

Read More

###### Asked in Prime Numbers, Numbers

### What are the two prime numbers that the product is an even number?

There are an infinite amount of such numbers.

Read More

###### Asked in Prime Numbers, Numbers

### Can you show all the prime numbers?

Impossible. The number is infinite.

Read More

###### Asked in Prime Numbers

### What numbers are divisible by four prime numbers?

2 * 3 * 5 * 7 = 210 is the smallest one divisible by four unique
prime numbers.
However, there are an infinite number of them, since there are
an infinite number of primes.
...

Read More

###### Asked in Prime Numbers

### Is there a 'biggest prime number'?

No. Euler roved that there are an infinite amount of prime
numbers.

Read More

###### Asked in Prime Numbers

### Do you think that there is one prime number which is the biggest of all?

No, I think prime numbers are infinite.

Read More

###### Asked in Prime Numbers

### Is 2 the only even prime number?

There are an infinite number of odd prime numbers, but 2 is the
only even prime .
...

Read More