What is the 321st prime number?
The 321st prime number is 2131. The next prime is 2137 (a gap of 6) and the one before is 2129.
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 321st one is 2131.
- 2
2131 is prime because no prime up to ā2131 ā 46.16 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 321st prime is close to 321 Ć ln(321) ā 1853, and here it is 2131.
- 4
2131 is a twin prime: 2129 and 2131 are both prime.
Primes around the 321st
| Position | Prime | Gap from the previous |
|---|---|---|
| 318 | 2111 | 12 |
| 319 | 2113 | 2 |
| 320 | 2129 | 16 |
| 321 | 2131 | 2 |
| 322 | 2137 | 6 |
| 323 | 2141 | 4 |
| 324 | 2143 | 2 |
Questions
What is the 321st prime number?
2131.
Which prime number is 2131?
2131 is the 321st prime number.
What is the sum of the first 321 primes?
314,284.