What is the 822nd prime number?
The 822nd prime number is 6317. The next prime is 6323 (a gap of 6) and the one before is 6311.
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 822nd one is 6317.
- 2
6317 is prime because no prime up to ā6317 ā 79.48 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 822nd prime is close to 822 Ć ln(822) ā 5517, and here it is 6317.
- 4
6317 has no twin: neither 6315 nor 6319 is prime.
Primes around the 822nd
| Position | Prime | Gap from the previous |
|---|---|---|
| 819 | 6299 | 12 |
| 820 | 6301 | 2 |
| 821 | 6311 | 10 |
| 822 | 6317 | 6 |
| 823 | 6323 | 6 |
| 824 | 6329 | 6 |
| 825 | 6337 | 8 |
Questions
What is the 822nd prime number?
6317.
Which prime number is 6317?
6317 is the 822nd prime number.
What is the sum of the first 822 primes?
2,415,165.