What is the 214th prime number?
The 214th prime number is 1307. The next prime is 1319 (a gap of 12) and the one before is 1303.
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 214th one is 1307.
- 2
1307 is prime because no prime up to ā1307 ā 36.15 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 214th prime is close to 214 Ć ln(214) ā 1148, and here it is 1307.
- 4
1307 has no twin: neither 1305 nor 1309 is prime.
Primes around the 214th
| Position | Prime | Gap from the previous |
|---|---|---|
| 211 | 1297 | 6 |
| 212 | 1301 | 4 |
| 213 | 1303 | 2 |
| 214 | 1307 | 4 |
| 215 | 1319 | 12 |
| 216 | 1321 | 2 |
| 217 | 1327 | 6 |
Questions
What is the 214th prime number?
1307.
Which prime number is 1307?
1307 is the 214th prime number.
What is the sum of the first 214 primes?
129,419.