What is the 1038th prime number?
The 1038th prime number is 8273. The next prime is 8287 (a gap of 14) and the one before is 8269.
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 1038th one is 8273.
- 2
8273 is prime because no prime up to ā8273 ā 90.96 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 1038th prime is close to 1038 Ć ln(1038) ā 7209, and here it is 8273.
- 4
8273 has no twin: neither 8271 nor 8275 is prime.
Primes around the 1038th
| Position | Prime | Gap from the previous |
|---|---|---|
| 1035 | 8243 | 6 |
| 1036 | 8263 | 20 |
| 1037 | 8269 | 6 |
| 1038 | 8273 | 4 |
| 1039 | 8287 | 14 |
| 1040 | 8291 | 4 |
| 1041 | 8293 | 2 |
Questions
What is the 1038th prime number?
8273.
Which prime number is 8273?
8273 is the 1038th prime number.
What is the sum of the first 1038 primes?
3,991,039.