What is the 4038th prime number?
The 4038th prime number is 38261. The next prime is 38273 (a gap of 12) and the one before is 38239.
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 4038th one is 38261.
- 2
38261 is prime because no prime up to ā38261 ā 195.60 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 4038th prime is close to 4038 Ć ln(4038) ā 33530, and here it is 38261.
- 4
38261 has no twin: neither 38259 nor 38263 is prime.
Primes around the 4038th
| Position | Prime | Gap from the previous |
|---|---|---|
| 4035 | 38231 | 12 |
| 4036 | 38237 | 6 |
| 4037 | 38239 | 2 |
| 4038 | 38261 | 22 |
| 4039 | 38273 | 12 |
| 4040 | 38281 | 8 |
| 4041 | 38287 | 6 |
Questions
What is the 4038th prime number?
38261.
Which prime number is 38261?
38261 is the 4038th prime number.
What is the sum of the first 4038 primes?
72,712,685.