What is the 405th prime number?
The 405th prime number is 2789. The next prime is 2791 (a gap of 2) and the one before is 2777.
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 405th one is 2789.
- 2
2789 is prime because no prime up to ā2789 ā 52.81 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 405th prime is close to 405 Ć ln(405) ā 2432, and here it is 2789.
- 4
2789 is a twin prime: 2789 and 2791 are both prime.
Primes around the 405th
| Position | Prime | Gap from the previous |
|---|---|---|
| 402 | 2753 | 4 |
| 403 | 2767 | 14 |
| 404 | 2777 | 10 |
| 405 | 2789 | 12 |
| 406 | 2791 | 2 |
| 407 | 2797 | 6 |
| 408 | 2801 | 4 |
Questions
What is the 405th prime number?
2789.
Which prime number is 2789?
2789 is the 405th prime number.
What is the sum of the first 405 primes?
521,660.