What is the 4138th prime number?
The 4138th prime number is 39313. The next prime is 39317 (a gap of 4) and the one before is 39301.
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 4138th one is 39313.
- 2
39313 is prime because no prime up to ā39313 ā 198.28 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 4138th prime is close to 4138 Ć ln(4138) ā 34461, and here it is 39313.
- 4
39313 has no twin: neither 39311 nor 39315 is prime.
Primes around the 4138th
| Position | Prime | Gap from the previous |
|---|---|---|
| 4135 | 39251 | 10 |
| 4136 | 39293 | 42 |
| 4137 | 39301 | 8 |
| 4138 | 39313 | 12 |
| 4139 | 39317 | 4 |
| 4140 | 39323 | 6 |
| 4141 | 39341 | 18 |
Questions
What is the 4138th prime number?
39313.
Which prime number is 39313?
39313 is the 4138th prime number.
What is the sum of the first 4138 primes?
76,592,845.