What is the 865th prime number?
The 865th prime number is 6703. The next prime is 6709 (a gap of 6) and the one before is 6701.
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 865th one is 6703.
- 2
6703 is prime because no prime up to ā6703 ā 81.87 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 865th prime is close to 865 Ć ln(865) ā 5850, and here it is 6703.
- 4
6703 is a twin prime: 6701 and 6703 are both prime.
Primes around the 865th
| Position | Prime | Gap from the previous |
|---|---|---|
| 862 | 6689 | 10 |
| 863 | 6691 | 2 |
| 864 | 6701 | 10 |
| 865 | 6703 | 2 |
| 866 | 6709 | 6 |
| 867 | 6719 | 10 |
| 868 | 6733 | 14 |
Questions
What is the 865th prime number?
6703.
Which prime number is 6703?
6703 is the 865th prime number.
What is the sum of the first 865 primes?
2,695,270.