What is the 82nd prime number?
The 82nd prime number is 421. The next prime is 431 (a gap of 10) and the one before is 419.
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 82nd one is 421.
- 2
421 is prime because no prime up to ā421 ā 20.52 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 82nd prime is close to 82 Ć ln(82) ā 361, and here it is 421.
- 4
421 is a twin prime: 419 and 421 are both prime.
Primes around the 82nd
| Position | Prime | Gap from the previous |
|---|---|---|
| 79 | 401 | 4 |
| 80 | 409 | 8 |
| 81 | 419 | 10 |
| 82 | 421 | 2 |
| 83 | 431 | 10 |
| 84 | 433 | 2 |
| 85 | 439 | 6 |
Questions
What is the 82nd prime number?
421.
Which prime number is 421?
421 is the 82nd prime number.
What is the sum of the first 82 primes?
15,537.