What is the 407th prime number?
The 407th prime number is 2797. The next prime is 2801 (a gap of 4) and the one before is 2791.
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 407th one is 2797.
- 2
2797 is prime because no prime up to ā2797 ā 52.89 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 407th prime is close to 407 Ć ln(407) ā 2446, and here it is 2797.
- 4
2797 has no twin: neither 2795 nor 2799 is prime.
Primes around the 407th
| Position | Prime | Gap from the previous |
|---|---|---|
| 404 | 2777 | 10 |
| 405 | 2789 | 12 |
| 406 | 2791 | 2 |
| 407 | 2797 | 6 |
| 408 | 2801 | 4 |
| 409 | 2803 | 2 |
| 410 | 2819 | 16 |
Questions
What is the 407th prime number?
2797.
Which prime number is 2797?
2797 is the 407th prime number.
What is the sum of the first 407 primes?
527,248.