What is the 613th prime number?
The 613th prime number is 4517. The next prime is 4519 (a gap of 2) and the one before is 4513.
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 613th one is 4517.
- 2
4517 is prime because no prime up to ā4517 ā 67.21 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 613th prime is close to 613 Ć ln(613) ā 3934, and here it is 4517.
- 4
4517 is a twin prime: 4517 and 4519 are both prime.
Primes around the 613th
| Position | Prime | Gap from the previous |
|---|---|---|
| 610 | 4493 | 10 |
| 611 | 4507 | 14 |
| 612 | 4513 | 6 |
| 613 | 4517 | 4 |
| 614 | 4519 | 2 |
| 615 | 4523 | 4 |
| 616 | 4547 | 24 |
Questions
What is the 613th prime number?
4517.
Which prime number is 4517?
4517 is the 613th prime number.
What is the sum of the first 613 primes?
1,281,192.