What is the 316th prime number?
The 316th prime number is 2089. The next prime is 2099 (a gap of 10) and the one before is 2087.
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 316th one is 2089.
- 2
2089 is prime because no prime up to ā2089 ā 45.71 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 316th prime is close to 316 Ć ln(316) ā 1819, and here it is 2089.
- 4
2089 is a twin prime: 2087 and 2089 are both prime.
Primes around the 316th
| Position | Prime | Gap from the previous |
|---|---|---|
| 313 | 2081 | 12 |
| 314 | 2083 | 2 |
| 315 | 2087 | 4 |
| 316 | 2089 | 2 |
| 317 | 2099 | 10 |
| 318 | 2111 | 12 |
| 319 | 2113 | 2 |
Questions
What is the 316th prime number?
2089.
Which prime number is 2089?
2089 is the 316th prime number.
What is the sum of the first 316 primes?
303,701.