What is the 51st prime number?
The 51st prime number is 233. The next prime is 239 (a gap of 6) and the one before is 229.
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 51st one is 233.
- 2
233 is prime because no prime up to ā233 ā 15.26 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 51st prime is close to 51 Ć ln(51) ā 201, and here it is 233.
- 4
233 has no twin: neither 231 nor 235 is prime.
Primes around the 51st
| Position | Prime | Gap from the previous |
|---|---|---|
| 48 | 223 | 12 |
| 49 | 227 | 4 |
| 50 | 229 | 2 |
| 51 | 233 | 4 |
| 52 | 239 | 6 |
| 53 | 241 | 2 |
| 54 | 251 | 10 |
Questions
What is the 51st prime number?
233.
Which prime number is 233?
233 is the 51st prime number.
What is the sum of the first 51 primes?
5,350.