What is the 3406th prime number?
The 3406th prime number is 31663. The next prime is 31667 (a gap of 4) and the one before is 31657.
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 3406th one is 31663.
- 2
31663 is prime because no prime up to ā31663 ā 177.94 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 3406th prime is close to 3406 Ć ln(3406) ā 27702, and here it is 31663.
- 4
31663 has no twin: neither 31661 nor 31665 is prime.
Primes around the 3406th
| Position | Prime | Gap from the previous |
|---|---|---|
| 3403 | 31643 | 16 |
| 3404 | 31649 | 6 |
| 3405 | 31657 | 8 |
| 3406 | 31663 | 6 |
| 3407 | 31667 | 4 |
| 3408 | 31687 | 20 |
| 3409 | 31699 | 12 |
Questions
What is the 3406th prime number?
31663.
Which prime number is 31663?
31663 is the 3406th prime number.
What is the sum of the first 3406 primes?
50,640,217.