What is the 5258th prime number?
The 5258th prime number is 51413. The next prime is 51419 (a gap of 6) and the one before is 51407.
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 5258th one is 51413.
- 2
51413 is prime because no prime up to ā51413 ā 226.74 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 5258th prime is close to 5258 Ć ln(5258) ā 45048, and here it is 51413.
- 4
51413 has no twin: neither 51411 nor 51415 is prime.
Primes around the 5258th
| Position | Prime | Gap from the previous |
|---|---|---|
| 5255 | 51361 | 12 |
| 5256 | 51383 | 22 |
| 5257 | 51407 | 24 |
| 5258 | 51413 | 6 |
| 5259 | 51419 | 6 |
| 5260 | 51421 | 2 |
| 5261 | 51427 | 6 |
Questions
What is the 5258th prime number?
51413.
Which prime number is 51413?
51413 is the 5258th prime number.
What is the sum of the first 5258 primes?
127,350,073.