No. By definition, a prime number must have exactly two distinct factors. 1 has only one factor (itself), so it is neither prime nor composite.

What is the largest known prime number?

As of 2024, the largest known prime has over 41 million digits — it is a Mersenne prime of the form 2^p - 1.

Are there infinitely many prime numbers?

Yes. Euclid proved around 300 BC that there are infinitely many primes, using a simple proof by contradiction.

What Is a Prime Number? Full List of Primes 1–100

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1. Definition of a Prime Number

A prime number is any natural number greater than 1 that cannot be divided evenly by any number other than 1 and itself. Examples: 2, 3, 5, 7, 11, 13...

A composite number has at least one additional factor. Examples: 4 (= 2×2), 6 (= 2×3), 9 (= 3×3).

The number 1 is neither prime nor composite — it is a special case.

The number 2 is the only even prime number. All other even numbers are divisible by 2, so they cannot be prime.

2. How to Test If a Number Is Prime

To test whether a number n is prime, check if it is divisible by any prime number up to √n. If none divide it evenly, n is prime.

Is 97 prime? √97 ≈ 9.85. Test primes up to 9: 2, 3, 5, 7. 97 ÷ 2 = 48.5 (no). 97 ÷ 3 = 32.33 (no). 97 ÷ 5 = 19.4 (no). 97 ÷ 7 = 13.86 (no). Therefore 97 is prime.

3. All Prime Numbers from 1 to 100

There are 25 prime numbers between 1 and 100:

{"".join(f'{p}' for p in [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])}

4. The Sieve of Eratosthenes

A systematic method invented by the ancient Greek mathematician Eratosthenes (~240 BC) for finding all primes up to any limit:

List all integers from 2 to your limit.
Start with the first number (2) and cross out all its multiples.
Move to the next uncrossed number (3) and cross out its multiples.
Continue until you've processed all numbers up to √limit.
All remaining uncrossed numbers are prime.

5. Why Primes Matter: RSA Cryptography

Modern internet security (HTTPS, banking, messaging) relies on the fact that multiplying two large primes is easy, but factoring the result back into those primes is computationally infeasible. RSA encryption uses primes with hundreds or thousands of digits.