What is the 238th prime number?
The 238th prime number is 1493. The next prime is 1499 (a gap of 6) and the one before is 1489.
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 238th one is 1493.
- 2
1493 is prime because no prime up to ā1493 ā 38.64 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 238th prime is close to 238 Ć ln(238) ā 1302, and here it is 1493.
- 4
1493 has no twin: neither 1491 nor 1495 is prime.
Primes around the 238th
| Position | Prime | Gap from the previous |
|---|---|---|
| 235 | 1483 | 2 |
| 236 | 1487 | 4 |
| 237 | 1489 | 2 |
| 238 | 1493 | 4 |
| 239 | 1499 | 6 |
| 240 | 1511 | 12 |
| 241 | 1523 | 12 |
Questions
What is the 238th prime number?
1493.
Which prime number is 1493?
1493 is the 238th prime number.
What is the sum of the first 238 primes?
163,541.