What is the 510th prime number?
The 510th prime number is 3643. The next prime is 3659 (a gap of 16) and the one before is 3637.
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 510th one is 3643.
- 2
3643 is prime because no prime up to ā3643 ā 60.36 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 510th prime is close to 510 Ć ln(510) ā 3180, and here it is 3643.
- 4
3643 has no twin: neither 3641 nor 3645 is prime.
Primes around the 510th
| Position | Prime | Gap from the previous |
|---|---|---|
| 507 | 3623 | 6 |
| 508 | 3631 | 8 |
| 509 | 3637 | 6 |
| 510 | 3643 | 6 |
| 511 | 3659 | 16 |
| 512 | 3671 | 12 |
| 513 | 3673 | 2 |
Questions
What is the 510th prime number?
3643.
Which prime number is 3643?
3643 is the 510th prime number.
What is the sum of the first 510 primes?
860,821.