What is the 311th prime number?
The 311th prime number is 2063. The next prime is 2069 (a gap of 6) and the one before is 2053.
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 311th one is 2063.
- 2
2063 is prime because no prime up to ā2063 ā 45.42 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 311th prime is close to 311 Ć ln(311) ā 1785, and here it is 2063.
- 4
2063 has no twin: neither 2061 nor 2065 is prime.
Primes around the 311th
| Position | Prime | Gap from the previous |
|---|---|---|
| 308 | 2029 | 2 |
| 309 | 2039 | 10 |
| 310 | 2053 | 14 |
| 311 | 2063 | 10 |
| 312 | 2069 | 6 |
| 313 | 2081 | 12 |
| 314 | 2083 | 2 |
Questions
What is the 311th prime number?
2063.
Which prime number is 2063?
2063 is the 311th prime number.
What is the sum of the first 311 primes?
293,292.