What is the 500th prime number?
The 500th prime number is 3571. The next prime is 3581 (a gap of 10) and the one before is 3559.
Position
Pick any whole number from 1 to 10,000.
How to work it out
- 1
List the primes in order: 2, 3, 5, 7, 11, 13, ā¦ The 500th one is 3571.
- 2
3571 is prime because no prime up to ā3571 ā 59.76 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 500th prime is close to 500 Ć ln(500) ā 3107, and here it is 3571.
- 4
3571 has no twin: neither 3569 nor 3573 is prime.
Primes around the 500th
| Position | Prime | Gap from the previous |
|---|---|---|
| 497 | 3547 | 6 |
| 498 | 3557 | 10 |
| 499 | 3559 | 2 |
| 500 | 3571 | 12 |
| 501 | 3581 | 10 |
| 502 | 3583 | 2 |
| 503 | 3593 | 10 |
Questions
What is the 500th prime number?
3571.
Which prime number is 3571?
3571 is the 500th prime number.
What is the sum of the first 500 primes?
824,693.