What is a Prime Number?

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Welcome to the Math Salamanders What is a Prime Number? page.

Hopefully all (or nearly all) your questions about prime numbers will be answered here!

There are also links to our prime number charts page and our prime number calculator.

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What is a prime number?

  • A prime number is a number that is only divisible by itself and 1.
  • It must also be greater than one.

Another way of saying this is that the only factors of a prime number are 1 and the number itself.

Examples of primes

11 is prime because its only factors are 1 and 11.

17 is prime because its only factors are 1 and 17.

53 is prime because its only factors are 1 and 53.



15 is NOT prime because it has 4 factors: 1, 3, 5 and 15.

28 is NOT prime because it has 6 factors: 1, 2, 4, 7, 14 and 28.

Prime Number Charts

On our Prime Number Charts page, we have many printable lists of prime numbers.

You can find the first 100 prime numbers, or print out a list of all prime numbers below 10,000.

We also have a prime number calculator which will find all the primes in a range that you set, and also a prime number tester which gives all the factors of a number, and tells you whether it is prime or not.

Is one a prime number?

The simple answer to this question is no.

Prime numbers have many different and interesting properties, which they would not have if the number one was prime.

Therefore, the number 1 was excluded from the set of prime numbers.

So the first prime number is 2.

Can prime numbers be negative?

The answer to this question is no.

All prime numbers belong to the set of natural numbers or positive integers.

Can prime numbers have a decimal or fraction value?

The answer to this question is again no.

All prime numbers belong to the set of natural numbers or positive integers.

They cannot be decimals or fractions.

Are some prime numbers even?

The answer to this question is yes.

However, there is only one even prime number which is 2.

No other even numbers can be prime as they will have 2 as a factor (as well as themselves and one).

What are the first 10 prime numbers?

The first ten prime numbers are...

2 3 5 7 11 13 17 19 23 29

What prime numbers are there between 1 and 100?

All the prime numbers between 1 and 100 are...

2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97

There are 25 prime numbers between 1 and 100.

What is the ...th prime number?

What is the ...th prime number?

Number

1st 2
10th 29
50th 229
100th 541
500th 3571
1,000th 7,919
10,000th 104,729

How man prime numbers are there between...

How many prime numbers between...

Number of Primes

Percentage

1 and 100

25

25%

1 and 1000

168

16.8%

1 and 10000

1229

12.3%

1 and 100,000

9592

9.6%

1 and 1,000,000

78498

7.8%

What this shows is that as the range of numbers gets large, the density of prime numbers gets smaller.

So the prime numbers become more spread out as the numbers get larger.

Are the prime numbers infinite?

So the next question I'm betting you want to know is: "If the prime numbers become more spread out as the numbers get larger and larger, do they eventually stop?"

Well, the answer is no.

The set of prime numbers is infinite and there are several different proofs to demonstrate this!

One such proof is given here on the primes.utm.edu website.

Sieve of Erastosthenes

The Sieve of Erastosthenes is a method for finding what is a prime numbers between 2 and any given number.

Eratosthenes was a Greek mathematician (as well as being a poet, an astronomer and musician) who lived from about 276BC to 194BC.

If you want to find out more about his sieve for finding primes, and print out some Sieve of Eratosthenes worksheets, use the link below.

What is a Prime Number ... Questions?

If you have any more questions about what is a prime number, or questions about primes, please feel free to leave us a comment below.

Alternatively, you can use the contact us form at the top and bottom of each page.

 

 

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