There are 168 prime numbers under 1000. The smallest one is 2, and the largest one below 1000 is 997.
A prime number under 1000 is a whole number less than 1000 with exactly two positive divisors: 1 and itself. That means 1 is not prime, 1000 is not prime, and every number in the list below passes the same divisor test.
Need to test one number instead of reading the full list? Use the Prime Number Checker to check whether a value is prime, composite, or outside the usual prime definition.
Prime Numbers Under 1000
The prime numbers under 1000 are:
1–99: 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
100–199: 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199
200–299: 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293
300–399: 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397
400–499: 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499
500–599: 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599
600–699: 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691
700–799: 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797
800–899: 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887
900–999: 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997
What “Under 1000” Means
Under 1000 means numbers that are less than 1000. The number 1000 itself is not included.
Even if someone reads the question as “up to 1000,” the list does not change, because 1000 is composite. It has many divisors, including 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, and 500.
Small but useful rule: 2 is the only even prime number. Every even number greater than 2 is divisible by 2, so it cannot be prime.
How Many Prime Numbers Are Under 1000?
There are 168 primes under 1000. They are not spread evenly across each group of 100 numbers. Some ranges contain more primes than others, and the gaps between primes slowly tend to widen as numbers grow.
| Range | Prime Count | First Prime in Range | Last Prime in Range |
|---|---|---|---|
| 1–99 | 25 | 2 | 97 |
| 100–199 | 21 | 101 | 199 |
| 200–299 | 16 | 211 | 293 |
| 300–399 | 16 | 307 | 397 |
| 400–499 | 17 | 401 | 499 |
| 500–599 | 14 | 503 | 599 |
| 600–699 | 16 | 601 | 691 |
| 700–799 | 14 | 701 | 797 |
| 800–899 | 15 | 809 | 887 |
| 900–999 | 14 | 907 | 997 |
Why These Numbers Are Prime
A number is prime when it has no positive divisors other than 1 and itself. For example, 997 is prime because no smaller prime divisor divides it evenly.
For numbers under 1000, you do not need to test every possible divisor. You only need to test prime divisors up to the square root of the number being checked.
Why the Square Root Test Works
If a number has a factor larger than its square root, it must also have a matching factor smaller than its square root. So if no divisor appears up to the square root, the number is prime.
Since the square root of 1000 is a little more than 31, every number under 1000 can be checked by testing divisibility only by these primes:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, and 31
That is why a prime list under 1000 is not just a memorized table. It follows a clear test.
Example: Checking 997
To check whether 997 is prime, test it against prime divisors up to 31:
- 997 is not even, so it is not divisible by 2.
- The digit sum is 25, so it is not divisible by 3.
- It does not end in 0 or 5, so it is not divisible by 5.
- It is not evenly divisible by 7, 11, 13, 17, 19, 23, 29, or 31.
Because no prime divisor up to 31 divides 997, 997 is prime.
Patterns in Prime Numbers Under 1000
Prime numbers are not random in the casual sense, but they also do not follow a simple repeating pattern. Under 1000, you can still notice several useful rules.
Most Prime Numbers Are Odd
Only one prime number is even: 2. Every other prime under 1000 is odd. This is one of the first filters used when checking primality.
No Prime Greater Than 5 Ends in 0 or 5
A number ending in 0 or 5 is divisible by 5. So after the prime number 5 itself, no prime can end with either digit.
Prime Numbers Greater Than 3 Fit the 6n ± 1 Shape
Every prime greater than 3 is one less or one more than a multiple of 6. For example:
- 29 = 6 × 5 − 1
- 31 = 6 × 5 + 1
- 997 = 6 × 166 + 1
This does not mean every number shaped like 6n − 1 or 6n + 1 is prime. For example, 25 and 35 fit that shape, but both are composite. The pattern is a filter, not a proof.
Prime and Composite Numbers Under 1000
Every whole number greater than 1 is either prime or composite. A prime number has exactly two positive divisors. A composite number has more than two.
For example, 31 is prime because its only positive divisors are 1 and 31. But 39 is composite because it can be written as 3 × 13.
This difference matters because prime numbers act as the basic factor pieces of whole numbers. For instance:
- 84 = 2 × 2 × 3 × 7
- 210 = 2 × 3 × 5 × 7
- 999 = 3 × 3 × 3 × 37
These examples show why prime numbers under 1000 are useful for learning factorization, divisibility, greatest common factors, least common multiples, and modular arithmetic.
Why 1 Is Not in the List
The number 1 is not prime because it has only one positive divisor: itself. A prime number must have exactly two positive divisors.
This rule keeps prime factorization clean. If 1 were treated as prime, a number such as 30 could be written as 2 × 3 × 5, or 1 × 2 × 3 × 5, or 1 × 1 × 2 × 3 × 5, and so on. The prime factorization would no longer be unique.
So the list of primes under 1000 starts with 2, not 1.
Why Prime Numbers Under 1000 Matter
Prime numbers under 1000 are small enough to inspect by hand, but large enough to show real prime behavior. They are often used in early number theory, programming exercises, classroom examples, and primality testing practice.
They Help Explain Divisibility
Checking primes under 1000 teaches fast divisibility habits. You learn when to test 2, 3, 5, 7, 11, and other small primes. This is more useful than memorizing a list without knowing why the numbers belong there.
They Connect to Factorization
Every composite number under 1000 can be broken into primes. This is why a prime list under 1000 works well beside a factorization tool or a prime checker. The list gives the reference; the tool gives the fast verification.
They Build Number Sense for Larger Primes
Large primes use more advanced tests, but the idea is still connected to the same question: does this number have a divisor other than 1 and itself? Small primes make that idea visible.
How to Check Any Number Under 1000
To decide whether a number under 1000 is prime, check whether it is divisible by any prime up to 31. If none of those primes divide it evenly, the number is prime.
Simple Check Process
- Make sure the number is greater than 1.
- If the number is 2, it is prime.
- If it is even and greater than 2, it is composite.
- Test divisibility by 3, 5, 7, 11, 13, 17, 19, 23, 29, and 31.
- If none divide evenly, the number is prime.
This process is short because numbers under 1000 have a small square-root limit. For larger values, a checker is faster and less error-prone.
Common Mistakes With Prime Numbers Under 1000
Counting 1 as Prime
1 is often mistaken for a prime number, but it is not prime. It has only one positive divisor.
Thinking All Odd Numbers Are Prime
Many odd numbers are composite. For example, 9, 15, 21, 25, 27, 33, 35, and 39 are all odd, but none of them are prime.
Assuming a Number Is Prime Because It Looks Unusual
Some numbers look prime at first but are not. For example, 989 may look prime, but it equals 23 × 43. Appearance is not enough. Divisibility decides.
Stopping the Test Too Early
For a number under 1000, checking only 2, 3, and 5 is not enough. You may also need to test 7, 11, 13, 17, 19, 23, 29, and 31.
FAQ About Prime Numbers Under 1000
How many prime numbers are under 1000?
There are 168 prime numbers under 1000.
What is the largest prime number under 1000?
The largest prime number under 1000 is 997.
What is the smallest prime number under 1000?
The smallest prime number under 1000 is 2. It is also the only even prime number.
Is 1 a prime number?
No. 1 is not prime because it has only one positive divisor. A prime number must have exactly two positive divisors.
Is 1000 a prime number?
No. 1000 is composite. It is divisible by 2, 4, 5, 8, 10, and many other numbers.
How do you check if a number under 1000 is prime?
Test whether it is divisible by prime numbers up to 31. If no prime divisor up to 31 divides it evenly, the number is prime.
Why do you only need to test divisors up to 31?
The square root of 1000 is a little more than 31. If a number under 1000 has a divisor, at least one divisor in the pair must be at or below its square root.