What is the 3404th prime number?
The 3404th prime number is 31649. The next prime is 31657 (a gap of 8) and the one before is 31643.
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 3404th one is 31649.
- 2
31649 is prime because no prime up to ā31649 ā 177.90 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 3404th prime is close to 3404 Ć ln(3404) ā 27684, and here it is 31649.
- 4
31649 has no twin: neither 31647 nor 31651 is prime.
Primes around the 3404th
| Position | Prime | Gap from the previous |
|---|---|---|
| 3401 | 31607 | 6 |
| 3402 | 31627 | 20 |
| 3403 | 31643 | 16 |
| 3404 | 31649 | 6 |
| 3405 | 31657 | 8 |
| 3406 | 31663 | 6 |
| 3407 | 31667 | 4 |
Questions
What is the 3404th prime number?
31649.
Which prime number is 31649?
31649 is the 3404th prime number.
What is the sum of the first 3404 primes?
50,576,897.