What is the 3413th prime number?
The 3413th prime number is 31729. The next prime is 31741 (a gap of 12) and the one before is 31727.
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 3413th one is 31729.
- 2
31729 is prime because no prime up to ā31729 ā 178.13 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 3413th prime is close to 3413 Ć ln(3413) ā 27766, and here it is 31729.
- 4
31729 is a twin prime: 31727 and 31729 are both prime.
Primes around the 3413th
| Position | Prime | Gap from the previous |
|---|---|---|
| 3410 | 31721 | 22 |
| 3411 | 31723 | 2 |
| 3412 | 31727 | 4 |
| 3413 | 31729 | 2 |
| 3414 | 31741 | 12 |
| 3415 | 31751 | 10 |
| 3416 | 31769 | 18 |
Questions
What is the 3413th prime number?
31729.
Which prime number is 31729?
31729 is the 3413th prime number.
What is the sum of the first 3413 primes?
50,862,170.