What is the 218th prime number?
The 218th prime number is 1361. The next prime is 1367 (a gap of 6) and the one before is 1327.
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 218th one is 1361.
- 2
1361 is prime because no prime up to ā1361 ā 36.89 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 218th prime is close to 218 Ć ln(218) ā 1174, and here it is 1361.
- 4
1361 has no twin: neither 1359 nor 1363 is prime.
Primes around the 218th
| Position | Prime | Gap from the previous |
|---|---|---|
| 215 | 1319 | 12 |
| 216 | 1321 | 2 |
| 217 | 1327 | 6 |
| 218 | 1361 | 34 |
| 219 | 1367 | 6 |
| 220 | 1373 | 6 |
| 221 | 1381 | 8 |
Questions
What is the 218th prime number?
1361.
Which prime number is 1361?
1361 is the 218th prime number.
What is the sum of the first 218 primes?
134,747.