What is the 342nd prime number?
The 342nd prime number is 2297. The next prime is 2309 (a gap of 12) and the one before is 2293.
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 342nd one is 2297.
- 2
2297 is prime because no prime up to ā2297 ā 47.93 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 342nd prime is close to 342 Ć ln(342) ā 1996, and here it is 2297.
- 4
2297 has no twin: neither 2295 nor 2299 is prime.
Primes around the 342nd
| Position | Prime | Gap from the previous |
|---|---|---|
| 339 | 2281 | 8 |
| 340 | 2287 | 6 |
| 341 | 2293 | 6 |
| 342 | 2297 | 4 |
| 343 | 2309 | 12 |
| 344 | 2311 | 2 |
| 345 | 2333 | 22 |
Questions
What is the 342nd prime number?
2297.
Which prime number is 2297?
2297 is the 342nd prime number.
What is the sum of the first 342 primes?
360,979.