What is the 3705th prime number?
The 3705th prime number is 34687. The next prime is 34693 (a gap of 6) and the one before is 34679.
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 3705th one is 34687.
- 2
34687 is prime because no prime up to ā34687 ā 186.24 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 3705th prime is close to 3705 Ć ln(3705) ā 30446, and here it is 34687.
- 4
34687 has no twin: neither 34685 nor 34689 is prime.
Primes around the 3705th
| Position | Prime | Gap from the previous |
|---|---|---|
| 3702 | 34667 | 16 |
| 3703 | 34673 | 6 |
| 3704 | 34679 | 6 |
| 3705 | 34687 | 8 |
| 3706 | 34693 | 6 |
| 3707 | 34703 | 10 |
| 3708 | 34721 | 18 |
Questions
What is the 3705th prime number?
34687.
Which prime number is 34687?
34687 is the 3705th prime number.
What is the sum of the first 3705 primes?
60,564,562.