Prime Numbers from 1 to 1000

Prime numbers 1 to 1000: there are 168 of them. The smallest is 2 and the largest is 997. A prime number has exactly two factors, 1 and itself, so each number in the chart below can only be divided evenly by 1 and by itself.

Prime numbers from 1 to 200

There are 46 prime numbers from 1 to 200. Here is the full 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, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199

The first 25 of these are below 100, and the other 21 are between 100 and 200.

Prime numbers from 100 to 200

There are 21 prime numbers from 100 to 200: 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199.

Since 100 and 200 are both even, they are not prime. So the list for 101 to 200 is exactly the same 21 numbers. Seven twin prime pairs sit in this range: (101, 103), (107, 109), (137, 139), (149, 151), (179, 181), (191, 193), (197, 199).

How many primes are in each hundred?

Primes thin out as numbers get bigger, but not in a perfectly smooth way. Here is the count for each block of one hundred:

Add them up and you get 168. The first hundred has the most primes, 25. Several later hundreds have only 14. There are 95 primes from 1 to 500, so 73 primes lie between 501 and 1000.

How to check if a number up to 1000 is prime

You only need to divide by primes up to the square root of the number. The square root of 1000 is about 31.6, so for any number up to 1000 you test at most these 11 primes: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 and 31.

1. Rule out even numbers (except 2) and numbers ending in 5 (except 5).
2. Add the digits. If the total divides by 3, so does the number.
3. Try 7, 11, 13 and the larger primes, stopping once the prime squared is bigger than your number.

Example: is 221 prime? It is odd, does not end in 5, and its digits add to 5, so 3 does not divide it. 7 and 11 do not divide it. But 13 does: 221 = 13 × 17. So 221 is composite. The table of 13 and table of 17 make this easy to spot.

Example: is 199 prime? Its square root is just over 14, so test 2, 3, 5, 7, 11 and 13. None divide 199, so it is prime.

Interesting facts about primes up to 1000

• The largest prime below 1000 is 997. The three largest are 983, 991 and 997.
• The first prime above 100 is 101, and 101 and 103 form a twin prime pair.
• There are 35 twin prime pairs below 1000.
• 1001 is not prime: 1001 = 7 × 11 × 13. Many people guess wrong on this one.
• Going further, there are 1229 primes below 10000.

For the smaller range with a colour chart and the sieve method, see prime numbers 1 to 100. To learn what makes a number prime, read about prime numbers and twin primes. You can also see how to write 101 in words or 1000 in words.

Try any number in the checker below. It also shows the prime factors of composite numbers.