What is the 56th prime number?
The 56th prime number is 263. The next prime is 269 (a gap of 6) and the one before is 257.
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 56th one is 263.
- 2
263 is prime because no prime up to ā263 ā 16.22 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 56th prime is close to 56 Ć ln(56) ā 225, and here it is 263.
- 4
263 has no twin: neither 261 nor 265 is prime.
Primes around the 56th
| Position | Prime | Gap from the previous |
|---|---|---|
| 53 | 241 | 2 |
| 54 | 251 | 10 |
| 55 | 257 | 6 |
| 56 | 263 | 6 |
| 57 | 269 | 6 |
| 58 | 271 | 2 |
| 59 | 277 | 6 |
Questions
What is the 56th prime number?
263.
Which prime number is 263?
263 is the 56th prime number.
What is the sum of the first 56 primes?
6,601.