What is the 312th prime number?
The 312th prime number is 2069. The next prime is 2081 (a gap of 12) and the one before is 2063.
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 312th one is 2069.
- 2
2069 is prime because no prime up to ā2069 ā 45.49 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 312th prime is close to 312 Ć ln(312) ā 1792, and here it is 2069.
- 4
2069 has no twin: neither 2067 nor 2071 is prime.
Primes around the 312th
| Position | Prime | Gap from the previous |
|---|---|---|
| 309 | 2039 | 10 |
| 310 | 2053 | 14 |
| 311 | 2063 | 10 |
| 312 | 2069 | 6 |
| 313 | 2081 | 12 |
| 314 | 2083 | 2 |
| 315 | 2087 | 4 |
Questions
What is the 312th prime number?
2069.
Which prime number is 2069?
2069 is the 312th prime number.
What is the sum of the first 312 primes?
295,361.