What is the 63rd prime number?
The 63rd prime number is 307. The next prime is 311 (a gap of 4) and the one before is 293.
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 63rd one is 307.
- 2
307 is prime because no prime up to ā307 ā 17.52 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 63rd prime is close to 63 Ć ln(63) ā 261, and here it is 307.
- 4
307 has no twin: neither 305 nor 309 is prime.
Primes around the 63rd
| Position | Prime | Gap from the previous |
|---|---|---|
| 60 | 281 | 4 |
| 61 | 283 | 2 |
| 62 | 293 | 10 |
| 63 | 307 | 14 |
| 64 | 311 | 4 |
| 65 | 313 | 2 |
| 66 | 317 | 4 |
Questions
What is the 63rd prime number?
307.
Which prime number is 307?
307 is the 63rd prime number.
What is the sum of the first 63 primes?
8,582.