What Are Prime Numbers? Definition, List & Easy Tricks

They’re the building blocks of every number you know—and they’ve fascinated mathematicians for thousands of years. If you’ve ever wondered what makes a number prime or how to explain it to a curious kid, this article breaks down the definition, gives you the full list up to 100, and shares practical tricks for spotting primes so you can teach—or learn—with confidence.

Smallest prime number: 2 · Only even prime number: 2 · Prime numbers up to 100: 25 · First five prime numbers: 2, 3, 5, 7, 11 · Largest known prime (as of 2024): 2^82,589,933 − 1

Here are the key facts about prime numbers at a glance:

What is a prime number?

Prime number definition in maths

• A prime number is a whole number greater than 1 that has exactly two factors: 1 and itself (BYJU’S (math education platform)).
• Prime numbers cannot be divided evenly by any number other than 1 and themselves (Britannica Kids (Tier 1 reference)).
• The number 1 is neither prime nor composite (Britannica Kids).
• Every whole number greater than 1 is either prime or can be uniquely built from primes—this is the Fundamental Theorem of Arithmetic (Think Academy (K–12 math enrichment)).

Examples of prime numbers

• The first five prime numbers are 2, 3, 5, 7, and 11 (Third Space Learning (teacher resource)).
• 2 is the only even prime number (BYJU’S).
• The first 10 prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29 (FirstCry (parenting & education)).

What this means: The definition is elegant—only two factors—yet it governs the entire structure of arithmetic. For students, grasping this simple rule opens the door to factors, multiples, and number theory.

What are prime numbers from 1 to 100?

Complete list of prime numbers up to 100

• The prime numbers from 1 to 100 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97 (BYJU’S).
• Notice that all primes after 2 are odd.

How many prime numbers are there between 1 and 100?

• There are 25 prime numbers between 1 and 100 (BYJU’S).
• That means one in every four numbers under 100 is prime.

The takeaway: Memorizing the 25 primes up to 100 is a classic starting point, but the real insight is that primes are scattered with no simple formula—only patterns like the 6k ± 1 rule.

How to check if a number is prime?

Simple divisibility test for prime numbers

• To check if a number is prime, test divisibility by all primes up to the square root of the number (Educational video (YouTube)).
• If a number has no divisors other than 1 and itself, it is prime.
• For example, to check 37: test divisibility by 2, 3, 5, 7 (since √37 ≈ 6.08). None divide evenly, so 37 is prime.

1. Check if the number is greater than 1. If not, it is not prime.
2. If the number is 2, it is prime (the only even prime).
3. If the number is even and greater than 2, it is composite.
4. Test divisibility by odd primes (3, 5, 7, 11, …) up to the square root of the number. If none divide evenly, the number is prime.

Quick tip to see if a number is prime

• One way to test whether a number is prime is to divide it by smaller prime numbers and check whether any division is exact (Educational video (YouTube)).
• The Sieve of Eratosthenes identifies primes by listing numbers, crossing out multiples of 2, 3, 5, and continuing (Think Academy (K–12 math enrichment)).

Why this matters: Being able to check primality by hand builds number sense. For students, it transforms an abstract definition into a practical skill they can use on homework and tests.

How to explain prime numbers to a child?

Kid-friendly definition of prime numbers

• Prime numbers are like building blocks that can only be made by multiplying 1 and themselves (Think Academy (K–12 math enrichment)).
• A prime number has exactly two factors (A Maths Dictionary for Kids (teacher tool)).
• The number 1 is neither prime nor composite—it’s special (Britannica Kids).

Activities to teach prime numbers

• Use visual aids like arrays or blocks to show that prime numbers cannot be arranged into rectangles other than a single row (FirstCry (parenting & education)).
• Color primes on a 1-to-100 chart (FirstCry).
• Use playing cards to create factor pairs—primes only make one pair (1 × itself).

The implication: Kids learn best when they can see and touch math. By physically creating arrays or coloring a hundred chart, the concept of “exactly two factors” becomes a concrete discovery rather than a memorized rule.

What is the trick to remember prime numbers?

Mnemonic devices for prime numbers

• One common trick is to remember that all prime numbers greater than 3 are of the form 6k ± 1 (Think Academy (K–12 math enrichment)).
• For example, 5 = 6×1 − 1, 7 = 6×1 + 1, 11 = 6×2 − 1, 13 = 6×2 + 1, and so on.
• But note: not every number of the form 6k ± 1 is prime (e.g., 25 = 6×4 + 1 is composite).

Easy way to learn prime numbers

• Memorize the primes up to 100 using patterns or songs (FirstCry (parenting & education)).
• A common mnemonic: “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.”
• Practice by listing primes in order, clapping on each prime.

The trade-off: Memory tricks save time but don’t replace understanding. For students who struggle with rote memorization, the 6k ± 1 rule offers a logical shortcut that reinforces number patterns.

These distinctions help avoid common misconceptions.

Voices on prime numbers

“A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers.”
— Wikipedia (community encyclopedia)

“A prime number is a whole number greater than 1 with only two factors – itself and 1.”
— Third Space Learning (teacher resource)

“There are infinitely many prime numbers.”
— Euclid (c. 300 BCE), as recorded in Elements

For students, parents, and teachers, the choice is clear: start with the definition, practice with the list up to 100, and use the divisibility test to check any number. The rest is pattern recognition—and that gets easier with time.

For more math learning resources, check out our Rate of Change Formula guide and Independent vs Dependent Variable explanation.

For a detailed breakdown of the concept, you can refer to this guide on prime numbers definition and list that includes a full list from 1 to 100.

Frequently asked questions