What is the 310th prime number?
The 310th prime number is 2053. The next prime is 2063 (a gap of 10) and the one before is 2039.
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 310th one is 2053.
- 2
2053 is prime because no prime up to ā2053 ā 45.31 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 310th prime is close to 310 Ć ln(310) ā 1778, and here it is 2053.
- 4
2053 has no twin: neither 2051 nor 2055 is prime.
Primes around the 310th
| Position | Prime | Gap from the previous |
|---|---|---|
| 307 | 2027 | 10 |
| 308 | 2029 | 2 |
| 309 | 2039 | 10 |
| 310 | 2053 | 14 |
| 311 | 2063 | 10 |
| 312 | 2069 | 6 |
| 313 | 2081 | 12 |
Questions
What is the 310th prime number?
2053.
Which prime number is 2053?
2053 is the 310th prime number.
What is the sum of the first 310 primes?
291,229.