What is the 3678th prime number?
The 3678th prime number is 34429. The next prime is 34439 (a gap of 10) and the one before is 34421.
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 3678th one is 34429.
- 2
34429 is prime because no prime up to ā34429 ā 185.55 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 3678th prime is close to 3678 Ć ln(3678) ā 30197, and here it is 34429.
- 4
34429 has no twin: neither 34427 nor 34431 is prime.
Primes around the 3678th
| Position | Prime | Gap from the previous |
|---|---|---|
| 3675 | 34381 | 12 |
| 3676 | 34403 | 22 |
| 3677 | 34421 | 18 |
| 3678 | 34429 | 8 |
| 3679 | 34439 | 10 |
| 3680 | 34457 | 18 |
| 3681 | 34469 | 12 |
Questions
What is the 3678th prime number?
34429.
Which prime number is 34429?
34429 is the 3678th prime number.
What is the sum of the first 3678 primes?
59,631,361.