The "Odd" One Out

What is the smallest prime number?

0 1 2 3 There is no smallest prime number.

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3 solutions

Atul Shivam
Jan 14, 2016

2 2 is the smallest prime number as 2 = 2 × 1 2=2×1 which has 2 common factors

(why not 1) as 1 = 1 × 1 1=1×1 which has only one factor 1 1 so its not a prime

(why not 3) as 3 3 is also a prime number but greater than 2 2 so its not the correct choice

Can negative numbers be a prime number?

Bill Grolz - 5 years, 2 months ago

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no! primes are integers greater than one with no positive divisors except one and itself

Atul Shivam - 5 years, 2 months ago

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I have seen the use of negative primes before though

Arulx Z - 4 years, 6 months ago

Well the definition of a prime number is that it has only two factors, 1 and itself. All negatives have 4 factors, 1, -1, n, and |n|. Unless you mean like -1

Tony Tu - 6 months ago

You should mention why zero is not prime to your solution.

. . - 2 months, 2 weeks ago
Prokash Shakkhar
Dec 12, 2016

Some people will choose the answer 1 1 at first glance.. But the reality is the number 1 1 has just only 1 1 divisor.. 1 = 1 1 1= 1*1 , So, 1 1 is neither prime nor composite.. But the number 2 2 has 2 divisors, ( 2 = 2 1 (2=2*1 ), which is the main characteristic of a prime number. Thus, 2 2 is the Smallest Prime Number \color{#E81990}\boxed{\text{Smallest Prime Number}} in the world being an even!

The definition I was given in school was that a prime number could only be divided by 1 and itself. With this definition 1 would be prime. Was the definition changed or were my teachers wrong?

Murrel Rhodes - 3 years, 3 months ago

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No, it's just the more standard one, while your teacher's definition made it easier for you to understand.

Samuel Godswill - 3 years ago

You have to mention why zero is not prime to your solution.

. . - 2 months, 2 weeks ago
. .
Mar 27, 2021

All numbers that a a must be a factor of zero.(It means that a 0 a | 0 ).

One only has one factor, 1, so 1 is not prime.

Two has only 2 factors, and so it is the smallest prime.

3 has 2 factors, but it is not the smallest, so it cannot be answered.

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