There are 168 prime numbers from 1 to 1000, and the list ends at 997. Even inside this small range, prime numbers reveal several ideas that matter in number theory: divisibility, factorization, prime gaps, and the way primes thin out as numbers rise. One detail comes first and stays first: 1 is neither prime nor composite. And 2 is the only even prime.
Prime Numbers From 1 to 1000
This reference table groups every prime by range, so the list is easy to scan without turning the page into a wall of digits. It also makes a useful pattern visible: the first hundred numbers contain more primes than the last hundred numbers in this table.
| Range | Prime Numbers | Count |
|---|---|---|
| 1–100 | 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97 | 25 |
| 101–200 | 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199 | 21 |
| 201–300 | 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293 | 16 |
| 301–400 | 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397 | 16 |
| 401–500 | 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499 | 17 |
| 501–600 | 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599 | 14 |
| 601–700 | 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691 | 16 |
| 701–800 | 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797 | 14 |
| 801–900 | 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887 | 15 |
| 901–1000 | 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997 | 14 |
- Smallest prime: 2
- Largest prime in this range: 997
- Total number of primes up to 1000: 168
- Prime count in the first hundred: 25
- Prime count in the last hundred of this table: 14
What Makes a Number Prime
A prime number is a natural number greater than 1 with exactly two positive divisors: 1 and itself. A composite number has more than two positive divisors. That definition looks short. Its reach is not. If you want to quickly verify whether a number is prime, you can use a prime number checker tool instead of testing divisibility manually.
Prime numbers act as the basic pieces of multiplication because every integer greater than 1 can be written as a product of primes, and that factorization is unique apart from order. In number theory, this is the Fundamental Theorem of Arithmetic.
That is also why 1 is excluded. If 1 were prime, the uniqueness of prime factorization would break apart at once: 6 could be written as 2 × 3, or 1 × 2 × 3, or 1 × 1 × 2 × 3, and so on. Small point, big effect.
Patterns Inside the Table
The Special Place of 2 and 5
2 is the only even prime because every other even number is divisible by 2. The number 5 has its own small distinction: it is the only prime that ends in 5. Any larger number ending in 5 is divisible by 5, so it cannot be prime.
Why Many Prime Candidates Fail
For numbers greater than 3, every prime fits the form 6k − 1 or 6k + 1. That rule helps explain the layout of the list, though it does not create primes by itself. Some numbers in those forms are still composite—25 and 35 are easy examples. So the pattern narrows the field; it does not settle the question.
How Prime Counts Change
Primes never stop, yet they do appear less often as numbers grow. The prime-counting function, written as π(x), records how many primes are less than or equal to a number x. In this range, π(10) = 4, π(100) = 25, and π(1000) = 168.
Later, the Prime Number Theorem explains this thinning in a broad way: as numbers become larger, the density of primes is close to 1 / ln(x). Not exact at each step, of course. Prime gaps jump around. Still, the long-run drift is clear even in a table this small.
List to 1000 and First 1000 Primes
These two phrases are not the same, and many readers mix them up. A list of prime numbers from 1 to 1000 contains every prime within that interval, so it stops at 997 and contains 168 values. The first 1000 prime numbers form a very different list; that sequence continues far beyond 1000, and its 1000th term is 7919.
Easy to miss, that distinction matters.
Related Prime Ideas
Twin Primes
Twin primes are pairs of primes that differ by 2, such as (3, 5), (11, 13), (17, 19), and (29, 31). This table contains many such pairs. In fact, there are 35 twin-prime pairs below 1000. Whether infinitely many twin primes exist remains an open question.
Mersenne Primes
A Mersenne prime has the form 2p − 1, where p is prime. Inside this range the Mersenne primes are 3, 7, 31, and 127. The pattern is famous because several record-size primes belong to this family, though many prime exponents p still produce composite values.
Fermat Primes
A Fermat prime has the form 22n + 1. Under 1000, the Fermat primes are 3, 5, 17, and 257. They appear rarely, and their scarcity makes them a recurring topic in number theory.
Co-Primes and Prime Factorization
Co-primes are pairs of integers with greatest common divisor 1. They do not have to be prime themselves: 8 and 15 are co-prime, even though both are composite. That distinction matters because prime numbers and co-primality meet constantly in modular arithmetic, fractions, and divisibility arguments.
Prime factorization sits nearby. Every composite number in the 1 to 1000 range breaks into primes in one way only, aside from order. For example, 840 = 23 × 3 × 5 × 7. Clean, exact, and very useful.
History and Modern Uses
Prime numbers have been studied for more than two thousand years. Euclid showed that there is no last prime number. Eratosthenes described a sieve that removes composites and leaves primes behind. Much later, analytic number theory began to explain how primes spread out across the integers.
- Euclid’s result: primes are infinite in number.
- Sieve of Eratosthenes: a classic way to filter out multiples and expose primes.
- Prime Number Theorem: a long-range description of how often primes appear.
- Modern computing: large primes support public-key cryptography, modular arithmetic, and primality testing.
The primes in this table are far too small for secure cryptographic systems, yet the same ideas appear there as well: factorization is hard in one direction, modular arithmetic stays orderly, and primes keep their special role.
FAQ
Is 1 a prime number?
No. A prime number must have exactly two positive divisors. The number 1 has only one positive divisor, so it is neither prime nor composite.
How many prime numbers are there from 1 to 1000?
There are 168 prime numbers from 1 to 1000.
What is the largest prime number below 1000?
The largest prime number below 1000 is 997.
Is every odd number prime?
No. Many odd numbers are composite, such as 9, 15, 21, 25, and 27. Being odd removes divisibility by 2, but that alone does not make a number prime.
Are all prime numbers greater than 3 of the form 6k ± 1?
Yes. Every prime greater than 3 fits that form. Still, not every number of the form 6k − 1 or 6k + 1 is prime.