What is the 314th prime number?
The 314th prime number is 2083. The next prime is 2087 (a gap of 4) and the one before is 2081.
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 314th one is 2083.
- 2
2083 is prime because no prime up to ā2083 ā 45.64 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 314th prime is close to 314 Ć ln(314) ā 1805, and here it is 2083.
- 4
2083 is a twin prime: 2081 and 2083 are both prime.
Primes around the 314th
| Position | Prime | Gap from the previous |
|---|---|---|
| 311 | 2063 | 10 |
| 312 | 2069 | 6 |
| 313 | 2081 | 12 |
| 314 | 2083 | 2 |
| 315 | 2087 | 4 |
| 316 | 2089 | 2 |
| 317 | 2099 | 10 |
Questions
What is the 314th prime number?
2083.
Which prime number is 2083?
2083 is the 314th prime number.
What is the sum of the first 314 primes?
299,525.