What is the 395th prime number?
The 395th prime number is 2711. The next prime is 2713 (a gap of 2) and the one before is 2707.
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 395th one is 2711.
- 2
2711 is prime because no prime up to ā2711 ā 52.07 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 395th prime is close to 395 Ć ln(395) ā 2362, and here it is 2711.
- 4
2711 is a twin prime: 2711 and 2713 are both prime.
Primes around the 395th
| Position | Prime | Gap from the previous |
|---|---|---|
| 392 | 2693 | 4 |
| 393 | 2699 | 6 |
| 394 | 2707 | 8 |
| 395 | 2711 | 4 |
| 396 | 2713 | 2 |
| 397 | 2719 | 6 |
| 398 | 2729 | 10 |
Questions
What is the 395th prime number?
2711.
Which prime number is 2711?
2711 is the 395th prime number.
What is the sum of the first 395 primes?
494,192.