What is the 3677th prime number?
The 3677th prime number is 34421. The next prime is 34429 (a gap of 8) and the one before is 34403.
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 3677th one is 34421.
- 2
34421 is prime because no prime up to ā34421 ā 185.53 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 3677th prime is close to 3677 Ć ln(3677) ā 30188, and here it is 34421.
- 4
34421 has no twin: neither 34419 nor 34423 is prime.
Primes around the 3677th
| Position | Prime | Gap from the previous |
|---|---|---|
| 3674 | 34369 | 2 |
| 3675 | 34381 | 12 |
| 3676 | 34403 | 22 |
| 3677 | 34421 | 18 |
| 3678 | 34429 | 8 |
| 3679 | 34439 | 10 |
| 3680 | 34457 | 18 |
Questions
What is the 3677th prime number?
34421.
Which prime number is 34421?
34421 is the 3677th prime number.
What is the sum of the first 3677 primes?
59,596,932.