What is the 538th prime number?
The 538th prime number is 3881. The next prime is 3889 (a gap of 8) and the one before is 3877.
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 538th one is 3881.
- 2
3881 is prime because no prime up to ā3881 ā 62.30 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 538th prime is close to 538 Ć ln(538) ā 3383, and here it is 3881.
- 4
3881 has no twin: neither 3879 nor 3883 is prime.
Primes around the 538th
| Position | Prime | Gap from the previous |
|---|---|---|
| 535 | 3853 | 2 |
| 536 | 3863 | 10 |
| 537 | 3877 | 14 |
| 538 | 3881 | 4 |
| 539 | 3889 | 8 |
| 540 | 3907 | 18 |
| 541 | 3911 | 4 |
Questions
What is the 538th prime number?
3881.
Which prime number is 3881?
3881 is the 538th prime number.
What is the sum of the first 538 primes?
966,335.