What is the 821st prime number?
The 821st prime number is 6311. The next prime is 6317 (a gap of 6) and the one before is 6301.
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 821st one is 6311.
- 2
6311 is prime because no prime up to ā6311 ā 79.44 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 821st prime is close to 821 Ć ln(821) ā 5509, and here it is 6311.
- 4
6311 has no twin: neither 6309 nor 6313 is prime.
Primes around the 821st
| Position | Prime | Gap from the previous |
|---|---|---|
| 818 | 6287 | 10 |
| 819 | 6299 | 12 |
| 820 | 6301 | 2 |
| 821 | 6311 | 10 |
| 822 | 6317 | 6 |
| 823 | 6323 | 6 |
| 824 | 6329 | 6 |
Questions
What is the 821st prime number?
6311.
Which prime number is 6311?
6311 is the 821st prime number.
What is the sum of the first 821 primes?
2,408,848.