What is the 317th prime number?
The 317th prime number is 2099. The next prime is 2111 (a gap of 12) and the one before is 2089.
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 317th one is 2099.
- 2
2099 is prime because no prime up to ā2099 ā 45.81 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 317th prime is close to 317 Ć ln(317) ā 1826, and here it is 2099.
- 4
2099 has no twin: neither 2097 nor 2101 is prime.
Primes around the 317th
| Position | Prime | Gap from the previous |
|---|---|---|
| 314 | 2083 | 2 |
| 315 | 2087 | 4 |
| 316 | 2089 | 2 |
| 317 | 2099 | 10 |
| 318 | 2111 | 12 |
| 319 | 2113 | 2 |
| 320 | 2129 | 16 |
Questions
What is the 317th prime number?
2099.
Which prime number is 2099?
2099 is the 317th prime number.
What is the sum of the first 317 primes?
305,800.