What is the 306th prime number?
The 306th prime number is 2017. The next prime is 2027 (a gap of 10) and the one before is 2011.
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 306th one is 2017.
- 2
2017 is prime because no prime up to ā2017 ā 44.91 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 306th prime is close to 306 Ć ln(306) ā 1751, and here it is 2017.
- 4
2017 has no twin: neither 2015 nor 2019 is prime.
Primes around the 306th
| Position | Prime | Gap from the previous |
|---|---|---|
| 303 | 1999 | 2 |
| 304 | 2003 | 4 |
| 305 | 2011 | 8 |
| 306 | 2017 | 6 |
| 307 | 2027 | 10 |
| 308 | 2029 | 2 |
| 309 | 2039 | 10 |
Questions
What is the 306th prime number?
2017.
Which prime number is 2017?
2017 is the 306th prime number.
What is the sum of the first 306 primes?
283,081.