Prime Numbers
A prime has exactly two factors: 1 and itself.
About this topic
A prime number has exactly two factors: 1 and itself. The first primes are 2, 3, 5, 7, 11 and 13. Numbers with more factors are called composite, and 1 is neither because it has only one factor. 2 is the only even prime.
Primes are the atoms of arithmetic, since every whole number above 1 can be built by multiplying primes. Euclid proved over two thousand years ago that there are infinitely many of them, and modern internet encryption still relies on how hard it is to factor huge numbers into primes.
To test whether a number such as 97 is prime, try dividing it by the primes up to its square root, here 2, 3, 5 and 7. None divides it, so 97 is prime. The Sieve of Eratosthenes does this for a whole table: cross out multiples of 2, then 3, then 5 and so on, and the survivors are prime.
Primes keep your online shopping and banking safe, because secure codes multiply two enormous primes together, and nobody can quickly undo that. Some insects, such as periodical cicadas, even emerge on prime-year cycles. A typical misconception is that all odd numbers are prime. Numbers like 9, 15 and 21 are odd but composite. Another is thinking 1 is prime, which would break the uniqueness of factorization.
Key ideas
- 2 is the only even prime
- 1 is not prime
- There are infinitely many primes
Quick check
Use cases: where Prime Numbers helps
- Homework: review the key idea behind Prime Numbers before you start a problem set.
- Exam revision: use the quick check to test whether you can recall Prime Numbers without notes.
- Visual learning: play with the interactive lab to see how Prime Numbers changes when you adjust its inputs.
- Teaching a friend: explain Prime Numbers in your own words, then compare your version with the key ideas.
Number and algebra skills are used in science, engineering, budgeting and computing.
Frequently asked questions
What is Prime Numbers?
A prime has exactly two factors: 1 and itself.
What will I learn in Prime Numbers?
2 is the only even prime. 1 is not prime. There are infinitely many primes.
Is Prime Numbers part of Mathematics?
Yes. It is one of 200 Mathematics topics on LearnViz HighSchoolEdu, with 3 key ideas, a live animation and a quick check.
Does the Prime Numbers lab work on a phone or tablet?
Yes. The animation resizes to fit your screen and supports touch, so you can drag, tap and slide with your finger.
How should I study Prime Numbers?
Read the summary and key ideas first, play with the interactive lab to see the idea in motion, then answer the quick check. If you get a question wrong, go back to the key idea it tests.
Do I need an account, and is my progress saved?
No account is needed. Marking a topic as learned is saved in your own browser, so it stays on that device and is not sent to a server.