What is the 814th prime number?
The 814th prime number is 6263. The next prime is 6269 (a gap of 6) and the one before is 6257.
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 814th one is 6263.
- 2
6263 is prime because no prime up to ā6263 ā 79.14 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 814th prime is close to 814 Ć ln(814) ā 5455, and here it is 6263.
- 4
6263 has no twin: neither 6261 nor 6265 is prime.
Primes around the 814th
| Position | Prime | Gap from the previous |
|---|---|---|
| 811 | 6229 | 8 |
| 812 | 6247 | 18 |
| 813 | 6257 | 10 |
| 814 | 6263 | 6 |
| 815 | 6269 | 6 |
| 816 | 6271 | 2 |
| 817 | 6277 | 6 |
Questions
What is the 814th prime number?
6263.
Which prime number is 6263?
6263 is the 814th prime number.
What is the sum of the first 814 primes?
2,364,833.