What is the 617th prime number?
The 617th prime number is 4549. The next prime is 4561 (a gap of 12) and the one before is 4547.
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 617th one is 4549.
- 2
4549 is prime because no prime up to ā4549 ā 67.45 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 617th prime is close to 617 Ć ln(617) ā 3964, and here it is 4549.
- 4
4549 is a twin prime: 4547 and 4549 are both prime.
Primes around the 617th
| Position | Prime | Gap from the previous |
|---|---|---|
| 614 | 4519 | 2 |
| 615 | 4523 | 4 |
| 616 | 4547 | 24 |
| 617 | 4549 | 2 |
| 618 | 4561 | 12 |
| 619 | 4567 | 6 |
| 620 | 4583 | 16 |
Questions
What is the 617th prime number?
4549.
Which prime number is 4549?
4549 is the 617th prime number.
What is the sum of the first 617 primes?
1,299,330.