What is the 84th prime number?
The 84th prime number is 433. The next prime is 439 (a gap of 6) and the one before is 431.
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 84th one is 433.
- 2
433 is prime because no prime up to ā433 ā 20.81 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 84th prime is close to 84 Ć ln(84) ā 372, and here it is 433.
- 4
433 is a twin prime: 431 and 433 are both prime.
Primes around the 84th
| Position | Prime | Gap from the previous |
|---|---|---|
| 81 | 419 | 10 |
| 82 | 421 | 2 |
| 83 | 431 | 10 |
| 84 | 433 | 2 |
| 85 | 439 | 6 |
| 86 | 443 | 4 |
| 87 | 449 | 6 |
Questions
What is the 84th prime number?
433.
Which prime number is 433?
433 is the 84th prime number.
What is the sum of the first 84 primes?
16,401.