What is the 81st prime number?
The 81st prime number is 419. The next prime is 421 (a gap of 2) and the one before is 409.
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 81st one is 419.
- 2
419 is prime because no prime up to ā419 ā 20.47 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 81st prime is close to 81 Ć ln(81) ā 356, and here it is 419.
- 4
419 is a twin prime: 419 and 421 are both prime.
Primes around the 81st
| Position | Prime | Gap from the previous |
|---|---|---|
| 78 | 397 | 8 |
| 79 | 401 | 4 |
| 80 | 409 | 8 |
| 81 | 419 | 10 |
| 82 | 421 | 2 |
| 83 | 431 | 10 |
| 84 | 433 | 2 |
Questions
What is the 81st prime number?
419.
Which prime number is 419?
419 is the 81st prime number.
What is the sum of the first 81 primes?
15,116.