What is the 827th prime number?
The 827th prime number is 6353. The next prime is 6359 (a gap of 6) and the one before is 6343.
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 827th one is 6353.
- 2
6353 is prime because no prime up to ā6353 ā 79.71 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 827th prime is close to 827 Ć ln(827) ā 5556, and here it is 6353.
- 4
6353 has no twin: neither 6351 nor 6355 is prime.
Primes around the 827th
| Position | Prime | Gap from the previous |
|---|---|---|
| 824 | 6329 | 6 |
| 825 | 6337 | 8 |
| 826 | 6343 | 6 |
| 827 | 6353 | 10 |
| 828 | 6359 | 6 |
| 829 | 6361 | 2 |
| 830 | 6367 | 6 |
Questions
What is the 827th prime number?
6353.
Which prime number is 6353?
6353 is the 827th prime number.
What is the sum of the first 827 primes?
2,446,850.