What is the 410th prime number?
The 410th prime number is 2819. The next prime is 2833 (a gap of 14) and the one before is 2803.
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 410th one is 2819.
- 2
2819 is prime because no prime up to ā2819 ā 53.09 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 410th prime is close to 410 Ć ln(410) ā 2467, and here it is 2819.
- 4
2819 has no twin: neither 2817 nor 2821 is prime.
Primes around the 410th
| Position | Prime | Gap from the previous |
|---|---|---|
| 407 | 2797 | 6 |
| 408 | 2801 | 4 |
| 409 | 2803 | 2 |
| 410 | 2819 | 16 |
| 411 | 2833 | 14 |
| 412 | 2837 | 4 |
| 413 | 2843 | 6 |
Questions
What is the 410th prime number?
2819.
Which prime number is 2819?
2819 is the 410th prime number.
What is the sum of the first 410 primes?
535,671.