What is the 357th prime number?
The 357th prime number is 2399. The next prime is 2411 (a gap of 12) and the one before is 2393.
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 357th one is 2399.
- 2
2399 is prime because no prime up to ā2399 ā 48.98 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 357th prime is close to 357 Ć ln(357) ā 2098, and here it is 2399.
- 4
2399 has no twin: neither 2397 nor 2401 is prime.
Primes around the 357th
| Position | Prime | Gap from the previous |
|---|---|---|
| 354 | 2383 | 2 |
| 355 | 2389 | 6 |
| 356 | 2393 | 4 |
| 357 | 2399 | 6 |
| 358 | 2411 | 12 |
| 359 | 2417 | 6 |
| 360 | 2423 | 6 |
Questions
What is the 357th prime number?
2399.
Which prime number is 2399?
2399 is the 357th prime number.
What is the sum of the first 357 primes?
396,360.