What is the 800th prime number?
The 800th prime number is 6133. The next prime is 6143 (a gap of 10) and the one before is 6131.
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 800th one is 6133.
- 2
6133 is prime because no prime up to ā6133 ā 78.31 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 800th prime is close to 800 Ć ln(800) ā 5348, and here it is 6133.
- 4
6133 is a twin prime: 6131 and 6133 are both prime.
Primes around the 800th
| Position | Prime | Gap from the previous |
|---|---|---|
| 797 | 6113 | 12 |
| 798 | 6121 | 8 |
| 799 | 6131 | 10 |
| 800 | 6133 | 2 |
| 801 | 6143 | 10 |
| 802 | 6151 | 8 |
| 803 | 6163 | 12 |
Questions
What is the 800th prime number?
6133.
Which prime number is 6133?
6133 is the 800th prime number.
What is the sum of the first 800 primes?
2,277,959.