What is the 240th prime number?
The 240th prime number is 1511. The next prime is 1523 (a gap of 12) and the one before is 1499.
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 240th one is 1511.
- 2
1511 is prime because no prime up to ā1511 ā 38.87 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 240th prime is close to 240 Ć ln(240) ā 1315, and here it is 1511.
- 4
1511 has no twin: neither 1509 nor 1513 is prime.
Primes around the 240th
| Position | Prime | Gap from the previous |
|---|---|---|
| 237 | 1489 | 2 |
| 238 | 1493 | 4 |
| 239 | 1499 | 6 |
| 240 | 1511 | 12 |
| 241 | 1523 | 12 |
| 242 | 1531 | 8 |
| 243 | 1543 | 12 |
Questions
What is the 240th prime number?
1511.
Which prime number is 1511?
1511 is the 240th prime number.
What is the sum of the first 240 primes?
166,551.