What is the 413th prime number?
The 413th prime number is 2843. The next prime is 2851 (a gap of 8) and the one before is 2837.
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 413th one is 2843.
- 2
2843 is prime because no prime up to ā2843 ā 53.32 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 413th prime is close to 413 Ć ln(413) ā 2488, and here it is 2843.
- 4
2843 has no twin: neither 2841 nor 2845 is prime.
Primes around the 413th
| Position | Prime | Gap from the previous |
|---|---|---|
| 410 | 2819 | 16 |
| 411 | 2833 | 14 |
| 412 | 2837 | 4 |
| 413 | 2843 | 6 |
| 414 | 2851 | 8 |
| 415 | 2857 | 6 |
| 416 | 2861 | 4 |
Questions
What is the 413th prime number?
2843.
Which prime number is 2843?
2843 is the 413th prime number.
What is the sum of the first 413 primes?
544,184.