Prime Numbers 1 to 100: Full List, Count and How to Find Them

The short answer

There are 25 prime numbers between 1 and 100: 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. The number 1 is not prime, and 2 is the only even prime. To list primes up to any limit from 10 to 1,000, open the List Primes tab of the Prime Number Checker and move the slider.

The full list, grouped by tens

A prime number is a whole number greater than 1 whose only factors are 1 and itself. Here are the primes up to 100, ten numbers at a time, which makes the list easier to memorise and check.

Range	Prime numbers	How many
1 to 10	2, 3, 5, 7	4
11 to 20	11, 13, 17, 19	4
21 to 30	23, 29	2
31 to 40	31, 37	2
41 to 50	41, 43, 47	3
51 to 60	53, 59	2
61 to 70	61, 67	2
71 to 80	71, 73, 79	3
81 to 90	83, 89	2
91 to 100	97	1

Notice how the primes thin out: there are 8 primes in the first 20 numbers, but only 1 between 91 and 100.

How many primes are there up to 200, 500 and 1,000?

These counts were worked out with a sieve program and match the tool's List Primes tab.

Up to	Number of primes	Largest prime in range
50	15	47
100	25	97
200	46	199
500	95	499
1,000	168	997

Between 101 and 200 there are 21 primes: 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197 and 199.

How to find the primes yourself: the Sieve of Eratosthenes

The sieve is the classic method taught in school, and it is the same idea the tool uses to build its list.

Write the numbers from 2 to 100 in a grid (a 10 × 10 grid works well).

Circle 2, the first prime. Cross out every other multiple of 2: 4, 6, 8 and so on.

Move to the next number that is not crossed out, which is 3. Circle it and cross out its multiples: 6, 9, 12 and so on (some are already crossed).

Do the same for 5 and then 7.

Stop there. Every number left uncrossed is prime.

Why can you stop at 7? Any composite number up to 100 must have a factor no bigger than its square root, and the square root of 100 is 10. The only primes below 10 are 2, 3, 5 and 7, so once their multiples are gone, nothing composite remains. For a list up to 1,000 you would need to sieve with every prime up to 31, because 31 × 31 = 961 and the next prime, 37, squared is above 1,000.

Quick checks for numbers that look prime

Some composite numbers fool people because they are odd and do not end in 5. These four come up often in exams:

• 51 = 3 × 17 (digits add to 6, so it divides by 3)
• 57 = 3 × 19 (digits add to 12)
• 87 = 3 × 29 (digits add to 15)
• 91 = 7 × 13

Useful divisibility rules for a quick test:

• By 2: the last digit is even.
• By 3: the digits add up to a multiple of 3.
• By 5: the last digit is 0 or 5.
• By 7: double the last digit and subtract it from the rest; if the result divides by 7, so does the number. For 91: 9 minus 2 = 7, so 91 divides by 7.

If you are unsure about a single number, type it into the Prime Checker tab. If it is not prime, the tool shows its prime factorisation, for example 91 = 7 × 13. For more on testing one number, see How to Check If a Number Is Prime (and Find Its Prime Factors).

Patterns worth knowing

• 2 is the only even prime. Every other even number divides by 2.
• After 5, every prime ends in 1, 3, 7 or 9. A number ending in 5 or an even digit cannot be prime (except 2 and 5 themselves). The reverse is not true: 21, 27, 33 and 39 end in those digits but are not prime.
• Twin primes are pairs that differ by 2. Below 100 they are (3, 5), (5, 7), (11, 13), (17, 19), (29, 31), (41, 43), (59, 61) and (71, 73).
• 24 of the 25 primes up to 100 are odd. Only 2 is even.

How to use the Lazyblink prime number tool

The tool has two tabs.

Prime Checker

Type a positive whole number into the box.

The result shows straight away whether it is prime.

For a composite number, it shows the prime factorisation, using ^ for powers (for example 72 = 2^3 × 3^2).

Quick buttons let you try 2, 17, 97, 127, 997 and 7919.

List Primes

Drag the slider to choose an upper limit between 10 and 1,000 (it moves in steps of 10).

The tool shows how many primes it found and lists them all.

Everything runs in your browser, so the answers appear instantly without a page reload.

Common mistakes

• Counting 1 as prime. A prime must have exactly two different factors. The number 1 has only one, so it is neither prime nor composite. The tool says this if you enter 1.
• Forgetting 2. Lists that start at 3 give 24 primes instead of 25.
• Assuming all odd numbers are prime. 9, 15, 21, 25, 27, 33, 35, 39, 45, 49 and the four numbers above are all odd composites below 100.
• Stopping the sieve too early for bigger ranges. Up to 100 you only need 2, 3, 5 and 7. Up to 200 you also need 11 and 13, because 13 × 13 = 169.

Where prime numbers are used

Primes are the building blocks of every whole number, which is why they matter for finding the HCF and LCM of numbers (see How to Find HCF and LCM of Two or More Numbers and the GCD and LCM Calculator) and for simplifying fractions. Large primes, hundreds of digits long, are also used in public-key encryption such as RSA.