What is a prime number?

A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. For example, 2, 3, 5, 7, 11, 13 are prime numbers. The number 1 is not considered prime.

How do you check if a number is prime?

To check if n is prime: 1) If n 2, it's not prime. 4) Check divisibility by odd numbers from 3 up to √n. If no divisor is found, n is prime.

What is prime factorization?

Prime factorization is expressing a number as a product of its prime factors. For example, 60 = 2² × 3 × 5. Every integer greater than 1 has a unique prime factorization (Fundamental Theorem of Arithmetic).

What is the difference between prime and composite numbers?

Prime numbers have exactly two factors: 1 and themselves. Composite numbers have more than two factors. For example, 7 is prime (factors: 1, 7), while 6 is composite (factors: 1, 2, 3, 6). The number 1 is neither prime nor composite.

Why is 2 the only even prime number?

2 is the only even prime because every other even number is divisible by 2, giving it at least three factors (1, 2, and itself). Since 2 only has factors 1 and 2, it's prime. This makes 2 unique among primes.

What is the largest known prime number?

The largest known prime numbers are Mersenne primes (2^p - 1). As of 2024, the largest known prime is 2^82,589,933 - 1, which has over 24 million digits. Finding large primes is important for cryptography.

Prime Number Checker

Prime numbers are the fundamental building blocks of all integers and underpin modern cryptography, including RSA encryption that secures online banking and communications. This tool lets you check primality, decompose any number into its prime factors, and generate prime lists within a range using the Sieve of Eratosthenes algorithm. Practical uses range from simplifying fractions and computing LCM/GCD to understanding digital security and solving number theory problems in competitive programming.

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Check Type

Number

First 25 Primes

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

Key Facts

• 2 is the only even prime

• 1 is neither prime nor composite

• Check divisibility up to √n

check_circle Result

✓

97 is PRIME

The 25th prime number

Previous Prime

Next Prime

101

Divisibility Test

√97 ≈ 9.85, check up to 9

97 ÷ 2 = 48.5 (not divisible)

97 ÷ 3 = 32.33 (not divisible)

97 ÷ 5 = 19.4 (not divisible)

97 ÷ 7 = 13.86 (not divisible)

→ No divisors found, 97 is prime

lightbulb Tips

•2 is the only even prime number
•1 is neither prime nor composite
•Check divisors only up to √n
•All primes > 3 are of form 6k±1

table_chart First 100 Primes

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, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541

Prime Facts

Primes ≤ 100: 25

Primes ≤ 1000: 168

Twin primes: (3,5), (5,7), (11,13), (17,19)...

How to Use This Calculator

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Choose Check Type

Check primality, factorize, find next/previous prime, or list primes.

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Enter Number

Input the number to check or use as starting point.

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Set Range (if needed)

For prime lists, enter the end of range.

visibility

View Results

See if prime, factors, or prime list with steps.

The Formula

A prime number has exactly two distinct positive divisors: 1 and itself. Testing divisibility up to √n is sufficient because factors come in pairs.

n is prime if its only divisors are 1 and n

lightbulb Variables Explained

Prime Number with exactly 2 divisors: 1 and itself
Composite Number with more than 2 divisors
√n Only need to check divisors up to square root

tips_and_updates Pro Tips

2 is the only even prime number - all other even numbers are divisible by 2

1 is neither prime nor composite by definition

To check if n is prime, only test divisibility up to √n

Twin primes are pairs differing by 2: (3,5), (5,7), (11,13), (17,19)...

All primes > 3 are of form 6k±1 (but not all 6k±1 are prime)

Prime factorization is unique for every number (Fundamental Theorem of Arithmetic)