What is the 57th prime number?
The 57th prime number is 269. The next prime is 271 (a gap of 2) and the one before is 263.
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 57th one is 269.
- 2
269 is prime because no prime up to ā269 ā 16.40 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 57th prime is close to 57 Ć ln(57) ā 230, and here it is 269.
- 4
269 is a twin prime: 269 and 271 are both prime.
Primes around the 57th
| Position | Prime | Gap from the previous |
|---|---|---|
| 54 | 251 | 10 |
| 55 | 257 | 6 |
| 56 | 263 | 6 |
| 57 | 269 | 6 |
| 58 | 271 | 2 |
| 59 | 277 | 6 |
| 60 | 281 | 4 |
Questions
What is the 57th prime number?
269.
Which prime number is 269?
269 is the 57th prime number.
What is the sum of the first 57 primes?
6,870.