What is the 406th prime number?
The 406th prime number is 2791. The next prime is 2797 (a gap of 6) and the one before is 2789.
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 406th one is 2791.
- 2
2791 is prime because no prime up to ā2791 ā 52.83 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 406th prime is close to 406 Ć ln(406) ā 2439, and here it is 2791.
- 4
2791 is a twin prime: 2789 and 2791 are both prime.
Primes around the 406th
| Position | Prime | Gap from the previous |
|---|---|---|
| 403 | 2767 | 14 |
| 404 | 2777 | 10 |
| 405 | 2789 | 12 |
| 406 | 2791 | 2 |
| 407 | 2797 | 6 |
| 408 | 2801 | 4 |
| 409 | 2803 | 2 |
Questions
What is the 406th prime number?
2791.
Which prime number is 2791?
2791 is the 406th prime number.
What is the sum of the first 406 primes?
524,451.