Prime Numbers – Definition with Examples
reviewed by Jo-ann Caballes
Updated on July 29, 2026
A prime number is a whole number greater than 1 that has exactly two factors: 1 and itself. That means a prime number cannot be divided evenly by any other whole number. The smallest prime number is 2 — it’s also the only even prime, since every other even number has a third factor (2) besides 1 and itself.
Prime numbers show up throughout arithmetic and algebra, and they’re also the basis of the encryption that keeps everyday technology secure. Understanding what makes a number prime — and having a few quick ways to check — makes a lot of later math easier.
This concept usually comes up around 4th to 6th grade, so if your child needs extra one-on-one practice with factors and primes, Brighterly’s elementary math tutors build number-theory basics like this one into a full curriculum.
What Are Prime Numbers?
A prime number is a natural number greater than 1 whose only two factors are 1 and the number itself — no other whole number divides into it evenly. Composite numbers, by contrast, always have a third factor. That single rule is what separates every prime from every other whole number.
Prime Number Definition
For example, 4 can be divided by 1, 2, and 4 — three factors — so 4 is not prime. But 5 can only be divided evenly by 1 and 5; dividing 5 by 2 gives 2.5, not a whole number. So 5 is prime.
Prime Number Examples
The prime numbers under 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 — 25 numbers in total. Every other whole number under 100 has at least one additional factor.
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Properties of Prime Numbers
Prime numbers share a handful of properties that make them easy to recognize once you know what to look for: every prime past 2 is odd, 2 is the only even prime, 1 is never counted as prime (it only has one factor, not two), and every whole number greater than 1 is either prime or can be broken down into a product of primes.
How to Find Prime Numbers: The Sieve of Eratosthenes
The fastest hand method for finding primes in a range is the Sieve of Eratosthenes: list the numbers, then systematically cross out every multiple of each prime you find, starting from 2. What’s left unmarked is prime.
- List every whole number from 2 up to the limit you want.
- Mark the first unmarked number as prime.
- Cross out every multiple of that number.
- Move to the next unmarked number and repeat.
- Stop once you pass the square root of your limit — everything still unmarked is prime.
For numbers up to 100, this takes just a few passes (crossing out multiples of 2, 3, 5, and 7 catches every composite number in that range). The method still works for larger ranges, but it takes more steps by hand.
Prime Factorization
Prime factorization is a second, complementary way to test whether a number is prime: break it into factors and count how many it has. A number with exactly two factors (1 and itself) is prime; a number with more than two is composite. For instance, 8 has four factors — 1, 2, 4, and 8 — so it’s composite.
One helpful shortcut: every prime number greater than 3 fits the form 6n + 1 or 6n − 1 for some whole number n. This is a necessary condition, not a guarantee — a handful of 6n ± 1 numbers are composite (25, 35, 49, 77, and 91 are the clearest examples under 100) — so it narrows the search but doesn’t replace checking for factors.
For a deeper look at breaking numbers into their prime building blocks, see these our full prime factorization guide, which walks through factor trees step by step.
Lists of Prime Numbers
There’s no complete list of primes — they continue infinitely — but here are the commonly referenced ranges.
Prime Numbers 1 to 100
There are 25 prime numbers between 1 and 100, listed above under “Prime Number Examples.”
Prime Numbers 1 to 200
Between 1 and 200, there are 46 prime numbers in total, including 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, and 199 in the 100–200 range alone.
Prime Numbers 1 to 1000
There are 168 prime numbers between 1 and 1000. Past this range, primes become steadily less frequent, though mathematicians have proven they never stop entirely — a result known since Euclid.
Prime vs. Composite Numbers
A prime number is a natural number greater than 1 with exactly two factors, while a composite number is a natural number greater than 1 with more than two factors. Looking at 1 through 6: 1 is neither prime nor composite (it has only one factor); 2 and 3 and 5 are prime; 4 and 6 are composite, since each can be divided in more than two ways.
For a full rundown of the other side of this comparison, see our guide to composite numbers, which covers the same 1–100 range from the opposite angle.
Solved Examples of Prime Numbers
Solved example 1
Which numbers from 1 to 25 are prime?
Answer: 2, 3, 5, 7, 11, 13, 17, 19, and 23 are the prime numbers from 1 to 25.
Solved example 2
Which numbers between 130 and 175 are prime?
Answer: 131, 137, 139, 149, 151, 157, 163, and 167 are prime. The same divisibility tests used for smaller numbers (checking 2, 3, 5, 7, and so on up to the square root of the number) still apply above 100.
Prime Numbers: Practice Problems
Note: The interactive quiz below uses fixed platform code and has been left unchanged.
Prime Numbers Worksheets
Put this into practice with related Brighterly worksheets:
- Prime and Composite Numbers Worksheets
- Factor Tree Worksheets
- Factors and Multiples Worksheets
- Greatest Common Factor Worksheets
Frequently Asked Questions on the Prime Number
Is 1 a Prime Number?
No. Even though 1 might seem like it could be prime, it isn’t. A prime number must have exactly two positive divisors, but 1 can only be divided by 1 itself — one divisor, not two. So it doesn’t qualify as prime, and it isn’t composite either; it’s in a category of its own.
Can a Prime Number Be Negative?
No. Prime numbers are always positive and start from 2. Negative numbers don’t fit the definition, since primes are defined as having exactly two positive divisors — a rule that only applies to natural numbers greater than 1.
What Is the Difference Between a Prime Number and a Co-Prime Number?
A prime number is a single number with no divisors except 1 and itself. Co-prime numbers, on the other hand, are a pair of numbers that share no common factor other than 1 — the numbers themselves don’t have to be prime. For example, 8 and 9 are co-prime even though neither is a prime number.
What Is the Smallest Prime Number?
2 is the smallest prime number, since it can only be divided by 1 and by itself. It’s also the only even prime number — every other even number has 2 as an extra factor, which disqualifies it.
Is Every Odd Number Prime?
No. While every prime number past 2 happens to be odd, not every odd number is prime. Nine, for example, is odd but composite, since it can be divided by 1, 3, and 9 — three factors instead of two.
How Do You Quickly Check if a Number Is Prime?
Test whether any whole number from 2 up to the square root of your number divides it evenly. If none do, the number is prime. For numbers under 100, checking divisibility by 2, 3, 5, and 7 is enough to confirm.
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