What is the 198th prime number?
The 198th prime number is 1213. The next prime is 1217 (a gap of 4) and the one before is 1201.
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 198th one is 1213.
- 2
1213 is prime because no prime up to ā1213 ā 34.83 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 198th prime is close to 198 Ć ln(198) ā 1047, and here it is 1213.
- 4
1213 has no twin: neither 1211 nor 1215 is prime.
Primes around the 198th
| Position | Prime | Gap from the previous |
|---|---|---|
| 195 | 1187 | 6 |
| 196 | 1193 | 6 |
| 197 | 1201 | 8 |
| 198 | 1213 | 12 |
| 199 | 1217 | 4 |
| 200 | 1223 | 6 |
| 201 | 1229 | 6 |
Questions
What is the 198th prime number?
1213.
Which prime number is 1213?
1213 is the 198th prime number.
What is the sum of the first 198 primes?
109,147.