What is the 813th prime number?
The 813th prime number is 6257. The next prime is 6263 (a gap of 6) and the one before is 6247.
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 813th one is 6257.
- 2
6257 is prime because no prime up to ā6257 ā 79.10 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 813th prime is close to 813 Ć ln(813) ā 5448, and here it is 6257.
- 4
6257 has no twin: neither 6255 nor 6259 is prime.
Primes around the 813th
| Position | Prime | Gap from the previous |
|---|---|---|
| 810 | 6221 | 4 |
| 811 | 6229 | 8 |
| 812 | 6247 | 18 |
| 813 | 6257 | 10 |
| 814 | 6263 | 6 |
| 815 | 6269 | 6 |
| 816 | 6271 | 2 |
Questions
What is the 813th prime number?
6257.
Which prime number is 6257?
6257 is the 813th prime number.
What is the sum of the first 813 primes?
2,358,570.