What is the 805th prime number?
The 805th prime number is 6197. The next prime is 6199 (a gap of 2) and the one before is 6173.
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 805th one is 6197.
- 2
6197 is prime because no prime up to ā6197 ā 78.72 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 805th prime is close to 805 Ć ln(805) ā 5386, and here it is 6197.
- 4
6197 is a twin prime: 6197 and 6199 are both prime.
Primes around the 805th
| Position | Prime | Gap from the previous |
|---|---|---|
| 802 | 6151 | 8 |
| 803 | 6163 | 12 |
| 804 | 6173 | 10 |
| 805 | 6197 | 24 |
| 806 | 6199 | 2 |
| 807 | 6203 | 4 |
| 808 | 6211 | 8 |
Questions
What is the 805th prime number?
6197.
Which prime number is 6197?
6197 is the 805th prime number.
What is the sum of the first 805 primes?
2,308,786.