What is the 230th prime number?
The 230th prime number is 1451. The next prime is 1453 (a gap of 2) and the one before is 1447.
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 230th one is 1451.
- 2
1451 is prime because no prime up to ā1451 ā 38.09 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 230th prime is close to 230 Ć ln(230) ā 1251, and here it is 1451.
- 4
1451 is a twin prime: 1451 and 1453 are both prime.
Primes around the 230th
| Position | Prime | Gap from the previous |
|---|---|---|
| 227 | 1433 | 4 |
| 228 | 1439 | 6 |
| 229 | 1447 | 8 |
| 230 | 1451 | 4 |
| 231 | 1453 | 2 |
| 232 | 1459 | 6 |
| 233 | 1471 | 12 |
Questions
What is the 230th prime number?
1451.
Which prime number is 1451?
1451 is the 230th prime number.
What is the sum of the first 230 primes?
151,725.