What is the 221st prime number?
The 221st prime number is 1381. The next prime is 1399 (a gap of 18) and the one before is 1373.
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 221st one is 1381.
- 2
1381 is prime because no prime up to ā1381 ā 37.16 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 221st prime is close to 221 Ć ln(221) ā 1193, and here it is 1381.
- 4
1381 has no twin: neither 1379 nor 1383 is prime.
Primes around the 221st
| Position | Prime | Gap from the previous |
|---|---|---|
| 218 | 1361 | 34 |
| 219 | 1367 | 6 |
| 220 | 1373 | 6 |
| 221 | 1381 | 8 |
| 222 | 1399 | 18 |
| 223 | 1409 | 10 |
| 224 | 1423 | 14 |
Questions
What is the 221st prime number?
1381.
Which prime number is 1381?
1381 is the 221st prime number.
What is the sum of the first 221 primes?
138,868.