What is the 345th prime number?
The 345th prime number is 2333. The next prime is 2339 (a gap of 6) and the one before is 2311.
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 345th one is 2333.
- 2
2333 is prime because no prime up to ā2333 ā 48.30 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 345th prime is close to 345 Ć ln(345) ā 2016, and here it is 2333.
- 4
2333 has no twin: neither 2331 nor 2335 is prime.
Primes around the 345th
| Position | Prime | Gap from the previous |
|---|---|---|
| 342 | 2297 | 4 |
| 343 | 2309 | 12 |
| 344 | 2311 | 2 |
| 345 | 2333 | 22 |
| 346 | 2339 | 6 |
| 347 | 2341 | 2 |
| 348 | 2347 | 6 |
Questions
What is the 345th prime number?
2333.
Which prime number is 2333?
2333 is the 345th prime number.
What is the sum of the first 345 primes?
367,932.