What is the 361st prime number?
The 361st prime number is 2437. The next prime is 2441 (a gap of 4) and the one before is 2423.
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 361st one is 2437.
- 2
2437 is prime because no prime up to ā2437 ā 49.37 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 361st prime is close to 361 Ć ln(361) ā 2126, and here it is 2437.
- 4
2437 has no twin: neither 2435 nor 2439 is prime.
Primes around the 361st
| Position | Prime | Gap from the previous |
|---|---|---|
| 358 | 2411 | 12 |
| 359 | 2417 | 6 |
| 360 | 2423 | 6 |
| 361 | 2437 | 14 |
| 362 | 2441 | 4 |
| 363 | 2447 | 6 |
| 364 | 2459 | 12 |
Questions
What is the 361st prime number?
2437.
Which prime number is 2437?
2437 is the 361st prime number.
What is the sum of the first 361 primes?
406,048.