What is the 8001st prime number?
The 8001st prime number is 81817. The next prime is 81839 (a gap of 22) and the one before is 81799.
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 8001st one is 81817.
- 2
81817 is prime because no prime up to ā81817 ā 286.04 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 8001st prime is close to 8001 Ć ln(8001) ā 71908, and here it is 81817.
- 4
81817 has no twin: neither 81815 nor 81819 is prime.
Primes around the 8001st
| Position | Prime | Gap from the previous |
|---|---|---|
| 7998 | 81769 | 8 |
| 7999 | 81773 | 4 |
| 8000 | 81799 | 26 |
| 8001 | 81817 | 18 |
| 8002 | 81839 | 22 |
| 8003 | 81847 | 8 |
| 8004 | 81853 | 6 |
Questions
What is the 8001st prime number?
81817.
Which prime number is 81817?
81817 is the 8001st prime number.
What is the sum of the first 8001 primes?
309,759,158.