There are 95 prime numbers from 1 to 500. The list begins with 2, the only even prime, and ends with 499. Every number in this set has exactly two positive divisors: 1 and itself. Nothing else divides it cleanly.
Prime Numbers 1 to 500: 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, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499.
The Full List of Prime Numbers from 1 to 500
The same list becomes easier to read when it is split into number ranges. This also shows how prime density changes as the numbers grow. Not evenly, though. Prime numbers thin out in a broad sense, yet small clusters still appear.
Prime Count and Distribution from 1 to 500
There are 25 primes from 1 to 100, but only 17 primes from 401 to 500. That drop does not mean primes follow a simple pattern. It only reflects a broad trend: as numbers get larger, composite numbers become more common because they can be formed by more possible factors.
| Range | Number of Primes | Smallest Prime | Largest Prime | Notes |
|---|---|---|---|---|
| 1–100 | 25 | 2 | 97 | Densest interval in this list |
| 101–200 | 21 | 101 | 199 | Several twin prime pairs appear |
| 201–300 | 16 | 211 | 293 | Includes the Fermat prime 257 |
| 301–400 | 16 | 307 | 397 | Contains the prime gap 317 to 331 |
| 401–500 | 17 | 401 | 499 | Ends with the largest prime under 500 |
What Makes a Number Prime?
A prime number is a whole number greater than 1 with exactly two positive divisors. For example, 13 is prime because only 1 and 13 divide it without a remainder. The number 15 is not prime because 3 and 5 divide it as well.
1 is not prime. It has only one positive divisor: itself. A prime needs exactly two. This small detail matters because it keeps prime factorization clear and unique.
The Special Role of 2
2 is the only even prime number. Every larger even number has 2 as a divisor, so it is composite. This is why the prime list from 1 to 500 turns odd immediately after 2.
Simple, but easy to miss.
Why 500 Is Not on the List
500 is composite because it has many divisors. One factorization is 500 = 2 × 2 × 5 × 5 × 5. Since it can be written as a product of smaller whole numbers, it cannot be prime.
The last prime before 500 is 499. To test 499, it is enough to check prime divisors up to its square root, because any larger factor would pair with a smaller one. Since √499 is a little above 22, the only prime divisors that matter are 2, 3, 5, 7, 11, 13, 17, and 19. None divide 499 exactly.
Prime Patterns Inside 1 to 500
Prime numbers do not line up in a neat repeating cycle, yet this range contains several visible patterns. Some are structural. Others are only local coincidences. Both matter, because they help readers see the difference between proven rules and observed behavior.
Final Digits of Primes Above 10
Every prime greater than 10 must end in 1, 3, 7, or 9. A number ending in 0, 2, 4, 6, or 8 is even. A number ending in 5 is divisible by 5. So those final digits are ruled out.
This rule does not prove a number is prime. It only removes obvious composites. For example, 49 ends in 9, but 49 = 7 × 7.
Twin Prime Pairs Under 500
Twin primes are pairs of prime numbers that differ by 2. The range from 1 to 500 contains 24 twin prime pairs:
- 3, 5
- 5, 7
- 11, 13
- 17, 19
- 29, 31
- 41, 43
- 59, 61
- 71, 73
- 101, 103
- 107, 109
- 137, 139
- 149, 151
- 179, 181
- 191, 193
- 197, 199
- 227, 229
- 239, 241
- 269, 271
- 281, 283
- 311, 313
- 347, 349
- 419, 421
- 431, 433
- 461, 463
The pair 3 and 5 is unusual because 3 is the only prime in the middle of two even numbers that still forms a twin pair on both sides: 3, 5 and 5, 7.
Prime Gaps in This Range
A prime gap is the distance between two neighboring primes. Small gaps appear often, especially gaps of 2, 4, and 6. In the range 1 to 500, the largest gap is 14. It appears between:
- 113 and 127
- 293 and 307
- 317 and 331
Between 113 and 127, every whole number is composite. Dense with factors, that small stretch is.
Related Prime Families Under 500
Some primes belong to named families because they fit a special formula or relationship. These families connect the simple list from 1 to 500 with deeper parts of number theory, including factorization, primality testing, and modular arithmetic.
Mersenne Primes Under 500
A Mersenne number has the form 2n − 1. When that number is prime, it is called a Mersenne prime. Under 500, the Mersenne primes are:
- 3
- 7
- 31
- 127
Not every number of the form 2n − 1 is prime. For example, 211 − 1 = 2047, and 2047 = 23 × 89. Formula first; proof after.
Fermat Primes Under 500
Fermat numbers have the form 22n + 1. The Fermat primes under 500 are:
- 3
- 5
- 17
- 257
The next Fermat number, 65537, is also prime, but it sits far outside the 1 to 500 range.
Sophie Germain and Safe Primes
A prime p is a Sophie Germain prime when 2p + 1 is also prime. The resulting prime 2p + 1 is called a safe prime. In this range, examples include:
- 11, because 2 × 11 + 1 = 23
- 23, because 2 × 23 + 1 = 47
- 83, because 2 × 83 + 1 = 167
- 233, because 2 × 233 + 1 = 467
This relationship shows how one prime can lead naturally to another. Prime structure often hides in pairs, chains, and factor rules.
Prime Factorization and the List from 1 to 500
Prime factorization writes a composite number as a product of prime numbers. The number 420, for instance, becomes 2 × 2 × 3 × 5 × 7. The order can change, but the prime factors themselves do not change.
This uniqueness is one reason prime numbers sit so close to the center of elementary number theory. A composite number may look ordinary, but its factorization points back to primes.
Examples from this range: 84 = 2 × 2 × 3 × 7, 121 = 11 × 11, 221 = 13 × 17, and 497 = 7 × 71. Each one is composite because it has positive divisors other than 1 and itself.
How the Sieve of Eratosthenes Explains This List
The Sieve of Eratosthenes is a classic way to generate all primes up to a chosen limit. For the limit 500, the method removes multiples of smaller primes and leaves the unmarked numbers. Since √500 is about 22.36, the needed base primes are 2, 3, 5, 7, 11, 13, 17, and 19.
After the multiples of those base primes are removed, the remaining numbers are exactly the primes from 1 to 500. The idea is efficient because every composite number up to 500 must have at least one prime factor at or below √500.
For a single number outside this list, the same divisibility idea appears in a more direct form through the prime number checker.
Common Misreadings in the 1 to 500 Range
Numbers That Look Prime but Are Composite
Some composite numbers are easy to mistake for primes because their factors are not obvious at first glance. A few examples:
- 91 = 7 × 13
- 119 = 7 × 17
- 143 = 11 × 13
- 169 = 13 × 13
- 221 = 13 × 17
- 391 = 17 × 23
- 493 = 17 × 29
These numbers pass simple “last digit” checks, yet they fail the divisor test. Ending in 1, 3, 7, or 9 is not enough.
Why 0, 1, and Negative Numbers Are Left Out
In the usual elementary definition, prime numbers are positive whole numbers greater than 1. That leaves out 0, 1, fractions, decimals, and negative numbers. Other areas of mathematics can extend the idea of primality to different number systems, but the list from 1 to 500 uses the standard whole-number definition.
FAQ About Prime Numbers from 1 to 500
How Many Prime Numbers Are There from 1 to 500?
There are 95 prime numbers from 1 to 500. The smallest is 2, and the largest is 499.
What Is the Largest Prime Number Less Than 500?
The largest prime number less than 500 is 499. It has no positive divisors other than 1 and 499.
Is 1 a Prime Number?
No. 1 is not a prime number because it has only one positive divisor. A prime number must have exactly two positive divisors.
Is 2 the Only Even Prime Number?
Yes. 2 is the only even prime number. Every other even number is divisible by 2, so it is composite.
How Many Twin Prime Pairs Are There Under 500?
There are 24 twin prime pairs from 1 to 500, including 3 and 5, 11 and 13, 101 and 103, and 461 and 463.
What Are the Prime Numbers Between 400 and 500?
The prime numbers between 400 and 500 are 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, and 499.