What is the 518th prime number?
The 518th prime number is 3709. The next prime is 3719 (a gap of 10) and the one before is 3701.
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 518th one is 3709.
- 2
3709 is prime because no prime up to ā3709 ā 60.90 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 518th prime is close to 518 Ć ln(518) ā 3237, and here it is 3709.
- 4
3709 has no twin: neither 3707 nor 3711 is prime.
Primes around the 518th
| Position | Prime | Gap from the previous |
|---|---|---|
| 515 | 3691 | 14 |
| 516 | 3697 | 6 |
| 517 | 3701 | 4 |
| 518 | 3709 | 8 |
| 519 | 3719 | 10 |
| 520 | 3727 | 8 |
| 521 | 3733 | 6 |
Questions
What is the 518th prime number?
3709.
Which prime number is 3709?
3709 is the 518th prime number.
What is the sum of the first 518 primes?
890,299.