What is the 397th prime number?
The 397th prime number is 2719. The next prime is 2729 (a gap of 10) and the one before is 2713.
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 397th one is 2719.
- 2
2719 is prime because no prime up to ā2719 ā 52.14 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 397th prime is close to 397 Ć ln(397) ā 2376, and here it is 2719.
- 4
2719 has no twin: neither 2717 nor 2721 is prime.
Primes around the 397th
| Position | Prime | Gap from the previous |
|---|---|---|
| 394 | 2707 | 8 |
| 395 | 2711 | 4 |
| 396 | 2713 | 2 |
| 397 | 2719 | 6 |
| 398 | 2729 | 10 |
| 399 | 2731 | 2 |
| 400 | 2741 | 10 |
Questions
What is the 397th prime number?
2719.
Which prime number is 2719?
2719 is the 397th prime number.
What is the sum of the first 397 primes?
499,624.