What is the 322nd prime number?
The 322nd prime number is 2137. The next prime is 2141 (a gap of 4) and the one before is 2131.
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 322nd one is 2137.
- 2
2137 is prime because no prime up to ā2137 ā 46.23 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 322nd prime is close to 322 Ć ln(322) ā 1859, and here it is 2137.
- 4
2137 has no twin: neither 2135 nor 2139 is prime.
Primes around the 322nd
| Position | Prime | Gap from the previous |
|---|---|---|
| 319 | 2113 | 2 |
| 320 | 2129 | 16 |
| 321 | 2131 | 2 |
| 322 | 2137 | 6 |
| 323 | 2141 | 4 |
| 324 | 2143 | 2 |
| 325 | 2153 | 10 |
Questions
What is the 322nd prime number?
2137.
Which prime number is 2137?
2137 is the 322nd prime number.
What is the sum of the first 322 primes?
316,421.