What is the 319th prime number?
The 319th prime number is 2113. The next prime is 2129 (a gap of 16) and the one before is 2111.
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 319th one is 2113.
- 2
2113 is prime because no prime up to ā2113 ā 45.97 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 319th prime is close to 319 Ć ln(319) ā 1839, and here it is 2113.
- 4
2113 is a twin prime: 2111 and 2113 are both prime.
Primes around the 319th
| Position | Prime | Gap from the previous |
|---|---|---|
| 316 | 2089 | 2 |
| 317 | 2099 | 10 |
| 318 | 2111 | 12 |
| 319 | 2113 | 2 |
| 320 | 2129 | 16 |
| 321 | 2131 | 2 |
| 322 | 2137 | 6 |
Questions
What is the 319th prime number?
2113.
Which prime number is 2113?
2113 is the 319th prime number.
What is the sum of the first 319 primes?
310,024.