What is the 398th prime number?
The 398th prime number is 2729. The next prime is 2731 (a gap of 2) and the one before is 2719.
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 398th one is 2729.
- 2
2729 is prime because no prime up to ā2729 ā 52.24 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 398th prime is close to 398 Ć ln(398) ā 2383, and here it is 2729.
- 4
2729 is a twin prime: 2729 and 2731 are both prime.
Primes around the 398th
| Position | Prime | Gap from the previous |
|---|---|---|
| 395 | 2711 | 4 |
| 396 | 2713 | 2 |
| 397 | 2719 | 6 |
| 398 | 2729 | 10 |
| 399 | 2731 | 2 |
| 400 | 2741 | 10 |
| 401 | 2749 | 8 |
Questions
What is the 398th prime number?
2729.
Which prime number is 2729?
2729 is the 398th prime number.
What is the sum of the first 398 primes?
502,353.