What is the 315th prime number?
The 315th prime number is 2087. The next prime is 2089 (a gap of 2) and the one before is 2083.
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 315th one is 2087.
- 2
2087 is prime because no prime up to ā2087 ā 45.68 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 315th prime is close to 315 Ć ln(315) ā 1812, and here it is 2087.
- 4
2087 is a twin prime: 2087 and 2089 are both prime.
Primes around the 315th
| Position | Prime | Gap from the previous |
|---|---|---|
| 312 | 2069 | 6 |
| 313 | 2081 | 12 |
| 314 | 2083 | 2 |
| 315 | 2087 | 4 |
| 316 | 2089 | 2 |
| 317 | 2099 | 10 |
| 318 | 2111 | 12 |
Questions
What is the 315th prime number?
2087.
Which prime number is 2087?
2087 is the 315th prime number.
What is the sum of the first 315 primes?
301,612.