What is the 8000th prime number?
The 8000th prime number is 81799. The next prime is 81817 (a gap of 18) and the one before is 81773.
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 8000th one is 81799.
- 2
81799 is prime because no prime up to ā81799 ā 286.01 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 8000th prime is close to 8000 Ć ln(8000) ā 71898, and here it is 81799.
- 4
81799 has no twin: neither 81797 nor 81801 is prime.
Primes around the 8000th
| Position | Prime | Gap from the previous |
|---|---|---|
| 7997 | 81761 | 12 |
| 7998 | 81769 | 8 |
| 7999 | 81773 | 4 |
| 8000 | 81799 | 26 |
| 8001 | 81817 | 18 |
| 8002 | 81839 | 22 |
| 8003 | 81847 | 8 |
Questions
What is the 8000th prime number?
81799.
Which prime number is 81799?
81799 is the 8000th prime number.
What is the sum of the first 8000 primes?
309,677,341.