What is the 825th prime number?
The 825th prime number is 6337. The next prime is 6343 (a gap of 6) and the one before is 6329.
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 825th one is 6337.
- 2
6337 is prime because no prime up to ā6337 ā 79.61 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 825th prime is close to 825 Ć ln(825) ā 5540, and here it is 6337.
- 4
6337 has no twin: neither 6335 nor 6339 is prime.
Primes around the 825th
| Position | Prime | Gap from the previous |
|---|---|---|
| 822 | 6317 | 6 |
| 823 | 6323 | 6 |
| 824 | 6329 | 6 |
| 825 | 6337 | 8 |
| 826 | 6343 | 6 |
| 827 | 6353 | 10 |
| 828 | 6359 | 6 |
Questions
What is the 825th prime number?
6337.
Which prime number is 6337?
6337 is the 825th prime number.
What is the sum of the first 825 primes?
2,434,154.