What is the 305th prime number?
The 305th prime number is 2011. The next prime is 2017 (a gap of 6) and the one before is 2003.
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 305th one is 2011.
- 2
2011 is prime because no prime up to ā2011 ā 44.84 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 305th prime is close to 305 Ć ln(305) ā 1745, and here it is 2011.
- 4
2011 has no twin: neither 2009 nor 2013 is prime.
Primes around the 305th
| Position | Prime | Gap from the previous |
|---|---|---|
| 302 | 1997 | 4 |
| 303 | 1999 | 2 |
| 304 | 2003 | 4 |
| 305 | 2011 | 8 |
| 306 | 2017 | 6 |
| 307 | 2027 | 10 |
| 308 | 2029 | 2 |
Questions
What is the 305th prime number?
2011.
Which prime number is 2011?
2011 is the 305th prime number.
What is the sum of the first 305 primes?
281,064.