How to Spot Prime Numbers Fast

A prime number has exactly two factors: 1 and itself. A few quick tests rule out most numbers instantly, so you can spot primes quickly.

1. 1. Remember the small primes

   The primes below 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.

2. 2. Rule out evens and fives

   Any number above 2 that ends in 0, 2, 4, 5, 6 or 8 is not prime. This removes about 60 percent of numbers right away.

3. 3. Use the digit-sum test for 3

   If the digits add up to a multiple of 3, the number divides by 3. For 51, 5 + 1 = 6, so 51 is not prime.

4. 4. Test 7 and 11

   For 11, subtract and add digits alternately: 121 gives 1 - 2 + 1 = 0, so 11 divides it. For 7, double the last digit and subtract it from the rest, then repeat.

5. 5. Stop at the square root

   To test a number, you only need to try primes up to its square root. For numbers under 100, that means checking 2, 3, 5 and 7.

Frequently asked questions

Is 1 a prime number?

No. A prime has exactly two factors, and 1 only has one.

Is 2 prime?

Yes. It is the only even prime number.

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