What is the 408th prime number?
The 408th prime number is 2801. The next prime is 2803 (a gap of 2) and the one before is 2797.
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 408th one is 2801.
- 2
2801 is prime because no prime up to ā2801 ā 52.92 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 408th prime is close to 408 Ć ln(408) ā 2453, and here it is 2801.
- 4
2801 is a twin prime: 2801 and 2803 are both prime.
Primes around the 408th
| Position | Prime | Gap from the previous |
|---|---|---|
| 405 | 2789 | 12 |
| 406 | 2791 | 2 |
| 407 | 2797 | 6 |
| 408 | 2801 | 4 |
| 409 | 2803 | 2 |
| 410 | 2819 | 16 |
| 411 | 2833 | 14 |
Questions
What is the 408th prime number?
2801.
Which prime number is 2801?
2801 is the 408th prime number.
What is the sum of the first 408 primes?
530,049.