What is the 509th prime number?
The 509th prime number is 3637. The next prime is 3643 (a gap of 6) and the one before is 3631.
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 509th one is 3637.
- 2
3637 is prime because no prime up to ā3637 ā 60.31 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 509th prime is close to 509 Ć ln(509) ā 3172, and here it is 3637.
- 4
3637 has no twin: neither 3635 nor 3639 is prime.
Primes around the 509th
| Position | Prime | Gap from the previous |
|---|---|---|
| 506 | 3617 | 4 |
| 507 | 3623 | 6 |
| 508 | 3631 | 8 |
| 509 | 3637 | 6 |
| 510 | 3643 | 6 |
| 511 | 3659 | 16 |
| 512 | 3671 | 12 |
Questions
What is the 509th prime number?
3637.
Which prime number is 3637?
3637 is the 509th prime number.
What is the sum of the first 509 primes?
857,178.