What is the 64th prime number?
The 64th prime number is 311. The next prime is 313 (a gap of 2) and the one before is 307.
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 64th one is 311.
- 2
311 is prime because no prime up to ā311 ā 17.64 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 64th prime is close to 64 Ć ln(64) ā 266, and here it is 311.
- 4
311 is a twin prime: 311 and 313 are both prime.
Primes around the 64th
| Position | Prime | Gap from the previous |
|---|---|---|
| 61 | 283 | 2 |
| 62 | 293 | 10 |
| 63 | 307 | 14 |
| 64 | 311 | 4 |
| 65 | 313 | 2 |
| 66 | 317 | 4 |
| 67 | 331 | 14 |
Questions
What is the 64th prime number?
311.
Which prime number is 311?
311 is the 64th prime number.
What is the sum of the first 64 primes?
8,893.