What is the 508th prime number?
The 508th prime number is 3631. The next prime is 3637 (a gap of 6) and the one before is 3623.
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 508th one is 3631.
- 2
3631 is prime because no prime up to ā3631 ā 60.26 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 508th prime is close to 508 Ć ln(508) ā 3165, and here it is 3631.
- 4
3631 has no twin: neither 3629 nor 3633 is prime.
Primes around the 508th
| Position | Prime | Gap from the previous |
|---|---|---|
| 505 | 3613 | 6 |
| 506 | 3617 | 4 |
| 507 | 3623 | 6 |
| 508 | 3631 | 8 |
| 509 | 3637 | 6 |
| 510 | 3643 | 6 |
| 511 | 3659 | 16 |
Questions
What is the 508th prime number?
3631.
Which prime number is 3631?
3631 is the 508th prime number.
What is the sum of the first 508 primes?
853,541.