What is the 213th prime number?
The 213th prime number is 1303. The next prime is 1307 (a gap of 4) and the one before is 1301.
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 213th one is 1303.
- 2
1303 is prime because no prime up to ā1303 ā 36.10 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 213th prime is close to 213 Ć ln(213) ā 1142, and here it is 1303.
- 4
1303 is a twin prime: 1301 and 1303 are both prime.
Primes around the 213th
| Position | Prime | Gap from the previous |
|---|---|---|
| 210 | 1291 | 2 |
| 211 | 1297 | 6 |
| 212 | 1301 | 4 |
| 213 | 1303 | 2 |
| 214 | 1307 | 4 |
| 215 | 1319 | 12 |
| 216 | 1321 | 2 |
Questions
What is the 213th prime number?
1303.
Which prime number is 1303?
1303 is the 213th prime number.
What is the sum of the first 213 primes?
128,112.