What is the 66th prime number?
The 66th prime number is 317. The next prime is 331 (a gap of 14) and the one before is 313.
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 66th one is 317.
- 2
317 is prime because no prime up to ā317 ā 17.80 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 66th prime is close to 66 Ć ln(66) ā 277, and here it is 317.
- 4
317 has no twin: neither 315 nor 319 is prime.
Primes around the 66th
| Position | Prime | Gap from the previous |
|---|---|---|
| 63 | 307 | 14 |
| 64 | 311 | 4 |
| 65 | 313 | 2 |
| 66 | 317 | 4 |
| 67 | 331 | 14 |
| 68 | 337 | 6 |
| 69 | 347 | 10 |
Questions
What is the 66th prime number?
317.
Which prime number is 317?
317 is the 66th prime number.
What is the sum of the first 66 primes?
9,523.