What is the 3680th prime number?
The 3680th prime number is 34457. The next prime is 34469 (a gap of 12) and the one before is 34439.
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 3680th one is 34457.
- 2
34457 is prime because no prime up to ā34457 ā 185.63 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 3680th prime is close to 3680 Ć ln(3680) ā 30215, and here it is 34457.
- 4
34457 has no twin: neither 34455 nor 34459 is prime.
Primes around the 3680th
| Position | Prime | Gap from the previous |
|---|---|---|
| 3677 | 34421 | 18 |
| 3678 | 34429 | 8 |
| 3679 | 34439 | 10 |
| 3680 | 34457 | 18 |
| 3681 | 34469 | 12 |
| 3682 | 34471 | 2 |
| 3683 | 34483 | 12 |
Questions
What is the 3680th prime number?
34457.
Which prime number is 34457?
34457 is the 3680th prime number.
What is the sum of the first 3680 primes?
59,700,257.