What is the 399th prime number?
The 399th prime number is 2731. The next prime is 2741 (a gap of 10) and the one before is 2729.
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 399th one is 2731.
- 2
2731 is prime because no prime up to ā2731 ā 52.26 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 399th prime is close to 399 Ć ln(399) ā 2390, and here it is 2731.
- 4
2731 is a twin prime: 2729 and 2731 are both prime.
Primes around the 399th
| Position | Prime | Gap from the previous |
|---|---|---|
| 396 | 2713 | 2 |
| 397 | 2719 | 6 |
| 398 | 2729 | 10 |
| 399 | 2731 | 2 |
| 400 | 2741 | 10 |
| 401 | 2749 | 8 |
| 402 | 2753 | 4 |
Questions
What is the 399th prime number?
2731.
Which prime number is 2731?
2731 is the 399th prime number.
What is the sum of the first 399 primes?
505,084.