What is the 205th prime number?
The 205th prime number is 1259. The next prime is 1277 (a gap of 18) and the one before is 1249.
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 205th one is 1259.
- 2
1259 is prime because no prime up to ā1259 ā 35.48 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 205th prime is close to 205 Ć ln(205) ā 1091, and here it is 1259.
- 4
1259 has no twin: neither 1257 nor 1261 is prime.
Primes around the 205th
| Position | Prime | Gap from the previous |
|---|---|---|
| 202 | 1231 | 2 |
| 203 | 1237 | 6 |
| 204 | 1249 | 12 |
| 205 | 1259 | 10 |
| 206 | 1277 | 18 |
| 207 | 1279 | 2 |
| 208 | 1283 | 4 |
Questions
What is the 205th prime number?
1259.
Which prime number is 1259?
1259 is the 205th prime number.
What is the sum of the first 205 primes?
117,792.