What is the 864th prime number?
The 864th prime number is 6701. The next prime is 6703 (a gap of 2) and the one before is 6691.
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 864th one is 6701.
- 2
6701 is prime because no prime up to ā6701 ā 81.86 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 864th prime is close to 864 Ć ln(864) ā 5842, and here it is 6701.
- 4
6701 is a twin prime: 6701 and 6703 are both prime.
Primes around the 864th
| Position | Prime | Gap from the previous |
|---|---|---|
| 861 | 6679 | 6 |
| 862 | 6689 | 10 |
| 863 | 6691 | 2 |
| 864 | 6701 | 10 |
| 865 | 6703 | 2 |
| 866 | 6709 | 6 |
| 867 | 6719 | 10 |
Questions
What is the 864th prime number?
6701.
Which prime number is 6701?
6701 is the 864th prime number.
What is the sum of the first 864 primes?
2,688,567.