What is the 65th prime number?
The 65th prime number is 313. The next prime is 317 (a gap of 4) and the one before is 311.
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 65th one is 313.
- 2
313 is prime because no prime up to ā313 ā 17.69 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 65th prime is close to 65 Ć ln(65) ā 271, and here it is 313.
- 4
313 is a twin prime: 311 and 313 are both prime.
Primes around the 65th
| Position | Prime | Gap from the previous |
|---|---|---|
| 62 | 293 | 10 |
| 63 | 307 | 14 |
| 64 | 311 | 4 |
| 65 | 313 | 2 |
| 66 | 317 | 4 |
| 67 | 331 | 14 |
| 68 | 337 | 6 |
Questions
What is the 65th prime number?
313.
Which prime number is 313?
313 is the 65th prime number.
What is the sum of the first 65 primes?
9,206.