What is the 3645th prime number?
The 3645th prime number is 34123. The next prime is 34127 (a gap of 4) and the one before is 34061.
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 3645th one is 34123.
- 2
34123 is prime because no prime up to ā34123 ā 184.72 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 3645th prime is close to 3645 Ć ln(3645) ā 29893, and here it is 34123.
- 4
34123 has no twin: neither 34121 nor 34125 is prime.
Primes around the 3645th
| Position | Prime | Gap from the previous |
|---|---|---|
| 3642 | 34039 | 6 |
| 3643 | 34057 | 18 |
| 3644 | 34061 | 4 |
| 3645 | 34123 | 62 |
| 3646 | 34127 | 4 |
| 3647 | 34129 | 2 |
| 3648 | 34141 | 12 |
Questions
What is the 3645th prime number?
34123.
Which prime number is 34123?
34123 is the 3645th prime number.
What is the sum of the first 3645 primes?
58,500,400.