What is the 540th prime number?
The 540th prime number is 3907. The next prime is 3911 (a gap of 4) and the one before is 3889.
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 540th one is 3907.
- 2
3907 is prime because no prime up to ā3907 ā 62.51 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 540th prime is close to 540 Ć ln(540) ā 3397, and here it is 3907.
- 4
3907 has no twin: neither 3905 nor 3909 is prime.
Primes around the 540th
| Position | Prime | Gap from the previous |
|---|---|---|
| 537 | 3877 | 14 |
| 538 | 3881 | 4 |
| 539 | 3889 | 8 |
| 540 | 3907 | 18 |
| 541 | 3911 | 4 |
| 542 | 3917 | 6 |
| 543 | 3919 | 2 |
Questions
What is the 540th prime number?
3907.
Which prime number is 3907?
3907 is the 540th prime number.
What is the sum of the first 540 primes?
974,131.