What is the 3665th prime number?
The 3665th prime number is 34301. The next prime is 34303 (a gap of 2) and the one before is 34297.
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 3665th one is 34301.
- 2
34301 is prime because no prime up to ā34301 ā 185.21 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 3665th prime is close to 3665 Ć ln(3665) ā 30077, and here it is 34301.
- 4
34301 is a twin prime: 34301 and 34303 are both prime.
Primes around the 3665th
| Position | Prime | Gap from the previous |
|---|---|---|
| 3662 | 34273 | 6 |
| 3663 | 34283 | 10 |
| 3664 | 34297 | 14 |
| 3665 | 34301 | 4 |
| 3666 | 34303 | 2 |
| 3667 | 34313 | 10 |
| 3668 | 34319 | 6 |
Questions
What is the 3665th prime number?
34301.
Which prime number is 34301?
34301 is the 3665th prime number.
What is the sum of the first 3665 primes?
59,184,680.