What is the 3405th prime number?
The 3405th prime number is 31657. The next prime is 31663 (a gap of 6) and the one before is 31649.
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 3405th one is 31657.
- 2
31657 is prime because no prime up to ā31657 ā 177.92 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 3405th prime is close to 3405 Ć ln(3405) ā 27693, and here it is 31657.
- 4
31657 has no twin: neither 31655 nor 31659 is prime.
Primes around the 3405th
| Position | Prime | Gap from the previous |
|---|---|---|
| 3402 | 31627 | 20 |
| 3403 | 31643 | 16 |
| 3404 | 31649 | 6 |
| 3405 | 31657 | 8 |
| 3406 | 31663 | 6 |
| 3407 | 31667 | 4 |
| 3408 | 31687 | 20 |
Questions
What is the 3405th prime number?
31657.
Which prime number is 31657?
31657 is the 3405th prime number.
What is the sum of the first 3405 primes?
50,608,554.