Prime numbers from 1 to 100

There are exactly 25 prime numbers between 1 and 100. A prime is a whole number greater than 1 whose only divisors are 1 and itself. Here they are, followed by a fast way to check any number up to 100 in your head.

The list

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

Chart of 1 to 100 (primes in bold)

How many primes in each group of ten

Test any number up to 120 in four checks

A number under 121 that isn't divisible by 2, 3, 5 or 7 (other than those four themselves) is prime. Any composite number has a factor no bigger than its square root, and the square root of 120 is under 11.

• 2: is it even?
• 3: do the digits add up to a multiple of 3?
• 5: does it end in 0 or 5?
• 7: the only check you actually have to work at. Knowing 49, 77 and 91 by heart covers most cases.

The divisibility rules guide covers these and the rules up to 12.

Numbers that look prime but aren't

They're all odd, none ends in 5, and none has a factor you'd spot at a glance, which is why they catch people out. Three of them fail the digit-sum test for 3.

Facts worth knowing

• 1 is not prime: a prime needs exactly two divisors.
• 2 is the only even prime.
• Every prime above 3 is one more or one less than a multiple of 6. The reverse isn't true: 25 = 24 + 1.
• There are 21 primes between 101 and 200: 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199.

Make the checks instant

Spotting primes is really just fast division. R3CK0N's division drill is timed and uses whole-number answers, which is the skill behind the checks above.