What is the 3407th prime number?
The 3407th prime number is 31667. The next prime is 31687 (a gap of 20) and the one before is 31663.
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 3407th one is 31667.
- 2
31667 is prime because no prime up to ā31667 ā 177.95 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 3407th prime is close to 3407 Ć ln(3407) ā 27711, and here it is 31667.
- 4
31667 has no twin: neither 31665 nor 31669 is prime.
Primes around the 3407th
| Position | Prime | Gap from the previous |
|---|---|---|
| 3404 | 31649 | 6 |
| 3405 | 31657 | 8 |
| 3406 | 31663 | 6 |
| 3407 | 31667 | 4 |
| 3408 | 31687 | 20 |
| 3409 | 31699 | 12 |
| 3410 | 31721 | 22 |
Questions
What is the 3407th prime number?
31667.
Which prime number is 31667?
31667 is the 3407th prime number.
What is the sum of the first 3407 primes?
50,671,884.