What is the 331st prime number?
The 331st prime number is 2221. The next prime is 2237 (a gap of 16) and the one before is 2213.
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 331st one is 2221.
- 2
2221 is prime because no prime up to ā2221 ā 47.13 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 331st prime is close to 331 Ć ln(331) ā 1921, and here it is 2221.
- 4
2221 has no twin: neither 2219 nor 2223 is prime.
Primes around the 331st
| Position | Prime | Gap from the previous |
|---|---|---|
| 328 | 2203 | 24 |
| 329 | 2207 | 4 |
| 330 | 2213 | 6 |
| 331 | 2221 | 8 |
| 332 | 2237 | 16 |
| 333 | 2239 | 2 |
| 334 | 2243 | 4 |
Questions
What is the 331st prime number?
2221.
Which prime number is 2221?
2221 is the 331st prime number.
What is the sum of the first 331 primes?
336,042.