What is the 89th prime number?
The 89th prime number is 461. The next prime is 463 (a gap of 2) and the one before is 457.
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 89th one is 461.
- 2
461 is prime because no prime up to ā461 ā 21.47 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 89th prime is close to 89 Ć ln(89) ā 399, and here it is 461.
- 4
461 is a twin prime: 461 and 463 are both prime.
Primes around the 89th
| Position | Prime | Gap from the previous |
|---|---|---|
| 86 | 443 | 4 |
| 87 | 449 | 6 |
| 88 | 457 | 8 |
| 89 | 461 | 4 |
| 90 | 463 | 2 |
| 91 | 467 | 4 |
| 92 | 479 | 12 |
Questions
What is the 89th prime number?
461.
Which prime number is 461?
461 is the 89th prime number.
What is the sum of the first 89 primes?
18,650.