What is the 3416th prime number?
The 3416th prime number is 31769. The next prime is 31771 (a gap of 2) and the one before is 31751.
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 3416th one is 31769.
- 2
31769 is prime because no prime up to ā31769 ā 178.24 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 3416th prime is close to 3416 Ć ln(3416) ā 27793, and here it is 31769.
- 4
31769 is a twin prime: 31769 and 31771 are both prime.
Primes around the 3416th
| Position | Prime | Gap from the previous |
|---|---|---|
| 3413 | 31729 | 2 |
| 3414 | 31741 | 12 |
| 3415 | 31751 | 10 |
| 3416 | 31769 | 18 |
| 3417 | 31771 | 2 |
| 3418 | 31793 | 22 |
| 3419 | 31799 | 6 |
Questions
What is the 3416th prime number?
31769.
Which prime number is 31769?
31769 is the 3416th prime number.
What is the sum of the first 3416 primes?
50,957,431.