What is the 5438th prime number?
The 5438th prime number is 53309. The next prime is 53323 (a gap of 14) and the one before is 53299.
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 5438th one is 53309.
- 2
53309 is prime because no prime up to ā53309 ā 230.89 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 5438th prime is close to 5438 Ć ln(5438) ā 46773, and here it is 53309.
- 4
53309 has no twin: neither 53307 nor 53311 is prime.
Primes around the 5438th
| Position | Prime | Gap from the previous |
|---|---|---|
| 5435 | 53279 | 10 |
| 5436 | 53281 | 2 |
| 5437 | 53299 | 18 |
| 5438 | 53309 | 10 |
| 5439 | 53323 | 14 |
| 5440 | 53327 | 4 |
| 5441 | 53353 | 26 |
Questions
What is the 5438th prime number?
53309.
Which prime number is 53309?
53309 is the 5438th prime number.
What is the sum of the first 5438 primes?
136,771,527.