What is the 542nd prime number?
The 542nd prime number is 3917. The next prime is 3919 (a gap of 2) and the one before is 3911.
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 542nd one is 3917.
- 2
3917 is prime because no prime up to ā3917 ā 62.59 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 542nd prime is close to 542 Ć ln(542) ā 3412, and here it is 3917.
- 4
3917 is a twin prime: 3917 and 3919 are both prime.
Primes around the 542nd
| Position | Prime | Gap from the previous |
|---|---|---|
| 539 | 3889 | 8 |
| 540 | 3907 | 18 |
| 541 | 3911 | 4 |
| 542 | 3917 | 6 |
| 543 | 3919 | 2 |
| 544 | 3923 | 4 |
| 545 | 3929 | 6 |
Questions
What is the 542nd prime number?
3917.
Which prime number is 3917?
3917 is the 542nd prime number.
What is the sum of the first 542 primes?
981,959.