What is the 517th prime number?
The 517th prime number is 3701. The next prime is 3709 (a gap of 8) and the one before is 3697.
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 517th one is 3701.
- 2
3701 is prime because no prime up to ā3701 ā 60.84 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 517th prime is close to 517 Ć ln(517) ā 3230, and here it is 3701.
- 4
3701 has no twin: neither 3699 nor 3703 is prime.
Primes around the 517th
| Position | Prime | Gap from the previous |
|---|---|---|
| 514 | 3677 | 4 |
| 515 | 3691 | 14 |
| 516 | 3697 | 6 |
| 517 | 3701 | 4 |
| 518 | 3709 | 8 |
| 519 | 3719 | 10 |
| 520 | 3727 | 8 |
Questions
What is the 517th prime number?
3701.
Which prime number is 3701?
3701 is the 517th prime number.
What is the sum of the first 517 primes?
886,590.