Prime Numbers – The Building Blocks of All Numbers

A prime number is a whole number greater than 1 that has exactly two factors: 1 and itself. Primes are the atoms of arithmetic — every other whole number can be broken down into them.

The hunt for primes never really stopped. The largest known prime numbers today are colossal Mersenne primes — numbers of the form 2ⁿ − 1 — found by the Great Internet Mersenne Prime Search (GIMPS), a volunteer computing project that has been running continuously since 1996. The current record holder, discovered in 2018, has more than 24 million digits; printed in an ordinary font it would stretch for tens of kilometres. And yet, thanks to Euclid’s 2,300-year-old proof mentioned below, we know for certain that no matter how large a prime anyone ever finds, there will always be a bigger one waiting.

Definition and Examples

First 25 Prime Numbers

The Sieve of Eratosthenes

A 2,200-year-old method for finding all primes up to any number:

1. List all numbers from 2 to your target.
2. Circle 2. Cross out all multiples of 2 (4, 6, 8...).
3. Circle the next uncrossed number (3). Cross out all its multiples.
4. Circle 5, cross out its multiples. Continue until done.
5. All circled numbers are prime.

How to Test if a Number Is Prime

Divide the number by all primes up to its square root. If none divide it exactly, it is prime.

Interesting Facts

• 2 is the only even prime number.
• There are infinitely many prime numbers (proved by Euclid ~300 BC).
• Primes underpin internet security — RSA encryption uses huge prime numbers.
• Twin primes differ by 2 (e.g. 11 and 13, 17 and 19).

Key Takeaways

Practice: Prime or Not?