What is the 309th prime number?
The 309th prime number is 2039. The next prime is 2053 (a gap of 14) and the one before is 2029.
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 309th one is 2039.
- 2
2039 is prime because no prime up to ā2039 ā 45.16 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 309th prime is close to 309 Ć ln(309) ā 1772, and here it is 2039.
- 4
2039 has no twin: neither 2037 nor 2041 is prime.
Primes around the 309th
| Position | Prime | Gap from the previous |
|---|---|---|
| 306 | 2017 | 6 |
| 307 | 2027 | 10 |
| 308 | 2029 | 2 |
| 309 | 2039 | 10 |
| 310 | 2053 | 14 |
| 311 | 2063 | 10 |
| 312 | 2069 | 6 |
Questions
What is the 309th prime number?
2039.
Which prime number is 2039?
2039 is the 309th prime number.
What is the sum of the first 309 primes?
289,176.