What is the 83rd prime number?
The 83rd prime number is 431. The next prime is 433 (a gap of 2) and the one before is 421.
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 83rd one is 431.
- 2
431 is prime because no prime up to ā431 ā 20.76 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 83rd prime is close to 83 Ć ln(83) ā 367, and here it is 431.
- 4
431 is a twin prime: 431 and 433 are both prime.
Primes around the 83rd
| Position | Prime | Gap from the previous |
|---|---|---|
| 80 | 409 | 8 |
| 81 | 419 | 10 |
| 82 | 421 | 2 |
| 83 | 431 | 10 |
| 84 | 433 | 2 |
| 85 | 439 | 6 |
| 86 | 443 | 4 |
Questions
What is the 83rd prime number?
431.
Which prime number is 431?
431 is the 83rd prime number.
What is the sum of the first 83 primes?
15,968.