What is the 3667th prime number?
The 3667th prime number is 34313. The next prime is 34319 (a gap of 6) and the one before is 34303.
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 3667th one is 34313.
- 2
34313 is prime because no prime up to ā34313 ā 185.24 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 3667th prime is close to 3667 Ć ln(3667) ā 30096, and here it is 34313.
- 4
34313 has no twin: neither 34311 nor 34315 is prime.
Primes around the 3667th
| Position | Prime | Gap from the previous |
|---|---|---|
| 3664 | 34297 | 14 |
| 3665 | 34301 | 4 |
| 3666 | 34303 | 2 |
| 3667 | 34313 | 10 |
| 3668 | 34319 | 6 |
| 3669 | 34327 | 8 |
| 3670 | 34337 | 10 |
Questions
What is the 3667th prime number?
34313.
Which prime number is 34313?
34313 is the 3667th prime number.
What is the sum of the first 3667 primes?
59,253,296.