What is the 350th prime number?
The 350th prime number is 2357. The next prime is 2371 (a gap of 14) and the one before is 2351.
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 350th one is 2357.
- 2
2357 is prime because no prime up to ā2357 ā 48.55 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 350th prime is close to 350 Ć ln(350) ā 2050, and here it is 2357.
- 4
2357 has no twin: neither 2355 nor 2359 is prime.
Primes around the 350th
| Position | Prime | Gap from the previous |
|---|---|---|
| 347 | 2341 | 2 |
| 348 | 2347 | 6 |
| 349 | 2351 | 4 |
| 350 | 2357 | 6 |
| 351 | 2371 | 14 |
| 352 | 2377 | 6 |
| 353 | 2381 | 4 |
Questions
What is the 350th prime number?
2357.
Which prime number is 2357?
2357 is the 350th prime number.
What is the sum of the first 350 primes?
379,667.