What is the 3540th prime number?
The 3540th prime number is 33023. The next prime is 33029 (a gap of 6) and the one before is 33013.
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 3540th one is 33023.
- 2
33023 is prime because no prime up to ā33023 ā 181.72 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 3540th prime is close to 3540 Ć ln(3540) ā 28928, and here it is 33023.
- 4
33023 has no twin: neither 33021 nor 33025 is prime.
Primes around the 3540th
| Position | Prime | Gap from the previous |
|---|---|---|
| 3537 | 32993 | 6 |
| 3538 | 32999 | 6 |
| 3539 | 33013 | 14 |
| 3540 | 33023 | 10 |
| 3541 | 33029 | 6 |
| 3542 | 33037 | 8 |
| 3543 | 33049 | 12 |
Questions
What is the 3540th prime number?
33023.
Which prime number is 33023?
33023 is the 3540th prime number.
What is the sum of the first 3540 primes?
54,977,833.