What is the 3675th prime number?
The 3675th prime number is 34381. The next prime is 34403 (a gap of 22) and the one before is 34369.
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 3675th one is 34381.
- 2
34381 is prime because no prime up to ā34381 ā 185.42 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 3675th prime is close to 3675 Ć ln(3675) ā 30169, and here it is 34381.
- 4
34381 has no twin: neither 34379 nor 34383 is prime.
Primes around the 3675th
| Position | Prime | Gap from the previous |
|---|---|---|
| 3672 | 34361 | 10 |
| 3673 | 34367 | 6 |
| 3674 | 34369 | 2 |
| 3675 | 34381 | 12 |
| 3676 | 34403 | 22 |
| 3677 | 34421 | 18 |
| 3678 | 34429 | 8 |
Questions
What is the 3675th prime number?
34381.
Which prime number is 34381?
34381 is the 3675th prime number.
What is the sum of the first 3675 primes?
59,528,108.