What is the 313th prime number?
The 313th prime number is 2081. The next prime is 2083 (a gap of 2) and the one before is 2069.
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 313th one is 2081.
- 2
2081 is prime because no prime up to ā2081 ā 45.62 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 313th prime is close to 313 Ć ln(313) ā 1799, and here it is 2081.
- 4
2081 is a twin prime: 2081 and 2083 are both prime.
Primes around the 313th
| Position | Prime | Gap from the previous |
|---|---|---|
| 310 | 2053 | 14 |
| 311 | 2063 | 10 |
| 312 | 2069 | 6 |
| 313 | 2081 | 12 |
| 314 | 2083 | 2 |
| 315 | 2087 | 4 |
| 316 | 2089 | 2 |
Questions
What is the 313th prime number?
2081.
Which prime number is 2081?
2081 is the 313th prime number.
What is the sum of the first 313 primes?
297,442.