What is the 409th prime number?
The 409th prime number is 2803. The next prime is 2819 (a gap of 16) and the one before is 2801.
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 409th one is 2803.
- 2
2803 is prime because no prime up to ā2803 ā 52.94 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 409th prime is close to 409 Ć ln(409) ā 2460, and here it is 2803.
- 4
2803 is a twin prime: 2801 and 2803 are both prime.
Primes around the 409th
| Position | Prime | Gap from the previous |
|---|---|---|
| 406 | 2791 | 2 |
| 407 | 2797 | 6 |
| 408 | 2801 | 4 |
| 409 | 2803 | 2 |
| 410 | 2819 | 16 |
| 411 | 2833 | 14 |
| 412 | 2837 | 4 |
Questions
What is the 409th prime number?
2803.
Which prime number is 2803?
2803 is the 409th prime number.
What is the sum of the first 409 primes?
532,852.