What is the 3643rd prime number?
The 3643rd prime number is 34057. The next prime is 34061 (a gap of 4) and the one before is 34039.
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 3643rd one is 34057.
- 2
34057 is prime because no prime up to ā34057 ā 184.55 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 3643rd prime is close to 3643 Ć ln(3643) ā 29875, and here it is 34057.
- 4
34057 has no twin: neither 34055 nor 34059 is prime.
Primes around the 3643rd
| Position | Prime | Gap from the previous |
|---|---|---|
| 3640 | 34031 | 12 |
| 3641 | 34033 | 2 |
| 3642 | 34039 | 6 |
| 3643 | 34057 | 18 |
| 3644 | 34061 | 4 |
| 3645 | 34123 | 62 |
| 3646 | 34127 | 4 |
Questions
What is the 3643rd prime number?
34057.
Which prime number is 34057?
34057 is the 3643rd prime number.
What is the sum of the first 3643 primes?
58,432,216.