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Study Guide · Maths

Smallest Prime Number

The smallest prime number is 2. It is also the only even prime number — all other even numbers are divisible by 2 and hence not prime. A prime number is a natural number greater than 1 that has exactly two factors: 1 and itself. 1 is NOT a prime number (it has only one factor).

Question (Click to Flip)

What is the smallest prime number?

Answer

The smallest prime number is 2. It is also the only even prime number — all other even numbers are divisible by 2, making them composite. 1 is not prime because it has only one factor. Prime numbers up to 10 are: 2, 3, 5, 7. There are 25 prime numbers between 1 and 100.

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Key Facts

Smallest prime number = 2.

2 is the only even prime number.

1 is NOT a prime number (it has only one factor).

Prime numbers up to 10: 2, 3, 5, 7.

There are 25 prime numbers between 1 and 100.

Fundamental Theorem of Arithmetic: every integer > 1 is prime or a product of primes.

Smallest Prime Number — Definition, Properties, and List

Smallest Prime Number: 2

Why is 2 the smallest prime? • 2 has exactly two factors: 1 and 2 • It satisfies the definition of a prime number • 1 is NOT prime because it has only one factor (1) • Every number < 2 (i.e., 1) is not prime by definition

Why is 2 special? • 2 is the ONLY even prime number • Every other even number is divisible by 2, making it composite • 2 is the first prime in the list of primes

Prime Numbers 1 to 100: 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 Total: 25 prime numbers between 1 and 100

Key Facts:

StatementAnswer
Smallest prime number2
Only even prime2
Is 1 a prime?No (only 1 factor)
Is 0 a prime?No
Smallest odd prime3
Largest 2-digit prime97
Prime numbers up to 102, 3, 5, 7
Twin primesPrimes differing by 2: (3,5), (5,7), (11,13)

Properties of Prime Numbers: • Every prime > 2 is odd • 2 is the only even prime • Two consecutive numbers cannot both be prime (except 2 and 3) • Every integer > 1 is either prime or can be expressed as a product of primes (Fundamental Theorem of Arithmetic) • There are infinitely many prime numbers (proved by Euclid)

How to Check if a Number is Prime: • Trial division: check if any number from 2 to √n divides n • Example: Is 37 prime? √37 ≈ 6.1 → check 2, 3, 5 — none divide 37 → 37 is prime

Questions and Answers

What is the smallest prime number?+

The smallest prime number is 2. It is also the only even prime number — all other even numbers are divisible by 2, making them composite. 1 is not prime because it has only one factor. Prime numbers up to 10 are: 2, 3, 5, 7. There are 25 prime numbers between 1 and 100.

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