What is the 8191st prime number?
The 8191st prime number is 84011. The next prime is 84017 (a gap of 6) and the one before is 83987.
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 8191st one is 84011.
- 2
84011 is prime because no prime up to ā84011 ā 289.85 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 8191st prime is close to 8191 Ć ln(8191) ā 73807, and here it is 84011.
- 4
84011 has no twin: neither 84009 nor 84013 is prime.
Primes around the 8191st
| Position | Prime | Gap from the previous |
|---|---|---|
| 8188 | 83969 | 30 |
| 8189 | 83983 | 14 |
| 8190 | 83987 | 4 |
| 8191 | 84011 | 24 |
| 8192 | 84017 | 6 |
| 8193 | 84047 | 30 |
| 8194 | 84053 | 6 |
Questions
What is the 8191st prime number?
84011.
Which prime number is 84011?
84011 is the 8191st prime number.
What is the sum of the first 8191 primes?
325,506,098.