What is the 396th prime number?
The 396th prime number is 2713. The next prime is 2719 (a gap of 6) and the one before is 2711.
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 396th one is 2713.
- 2
2713 is prime because no prime up to ā2713 ā 52.09 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 396th prime is close to 396 Ć ln(396) ā 2369, and here it is 2713.
- 4
2713 is a twin prime: 2711 and 2713 are both prime.
Primes around the 396th
| Position | Prime | Gap from the previous |
|---|---|---|
| 393 | 2699 | 6 |
| 394 | 2707 | 8 |
| 395 | 2711 | 4 |
| 396 | 2713 | 2 |
| 397 | 2719 | 6 |
| 398 | 2729 | 10 |
| 399 | 2731 | 2 |
Questions
What is the 396th prime number?
2713.
Which prime number is 2713?
2713 is the 396th prime number.
What is the sum of the first 396 primes?
496,905.