What is the 3409th prime number?
The 3409th prime number is 31699. The next prime is 31721 (a gap of 22) and the one before is 31687.
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 3409th one is 31699.
- 2
31699 is prime because no prime up to ā31699 ā 178.04 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 3409th prime is close to 3409 Ć ln(3409) ā 27729, and here it is 31699.
- 4
31699 has no twin: neither 31697 nor 31701 is prime.
Primes around the 3409th
| Position | Prime | Gap from the previous |
|---|---|---|
| 3406 | 31663 | 6 |
| 3407 | 31667 | 4 |
| 3408 | 31687 | 20 |
| 3409 | 31699 | 12 |
| 3410 | 31721 | 22 |
| 3411 | 31723 | 2 |
| 3412 | 31727 | 4 |
Questions
What is the 3409th prime number?
31699.
Which prime number is 31699?
31699 is the 3409th prime number.
What is the sum of the first 3409 primes?
50,735,270.