What is the 3642nd prime number?
The 3642nd prime number is 34039. The next prime is 34057 (a gap of 18) and the one before is 34033.
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 3642nd one is 34039.
- 2
34039 is prime because no prime up to ā34039 ā 184.50 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 3642nd prime is close to 3642 Ć ln(3642) ā 29865, and here it is 34039.
- 4
34039 has no twin: neither 34037 nor 34041 is prime.
Primes around the 3642nd
| Position | Prime | Gap from the previous |
|---|---|---|
| 3639 | 34019 | 22 |
| 3640 | 34031 | 12 |
| 3641 | 34033 | 2 |
| 3642 | 34039 | 6 |
| 3643 | 34057 | 18 |
| 3644 | 34061 | 4 |
| 3645 | 34123 | 62 |
Questions
What is the 3642nd prime number?
34039.
Which prime number is 34039?
34039 is the 3642nd prime number.
What is the sum of the first 3642 primes?
58,398,159.