What is the 412th prime number?
The 412th prime number is 2837. The next prime is 2843 (a gap of 6) and the one before is 2833.
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 412th one is 2837.
- 2
2837 is prime because no prime up to ā2837 ā 53.26 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 412th prime is close to 412 Ć ln(412) ā 2481, and here it is 2837.
- 4
2837 has no twin: neither 2835 nor 2839 is prime.
Primes around the 412th
| Position | Prime | Gap from the previous |
|---|---|---|
| 409 | 2803 | 2 |
| 410 | 2819 | 16 |
| 411 | 2833 | 14 |
| 412 | 2837 | 4 |
| 413 | 2843 | 6 |
| 414 | 2851 | 8 |
| 415 | 2857 | 6 |
Questions
What is the 412th prime number?
2837.
Which prime number is 2837?
2837 is the 412th prime number.
What is the sum of the first 412 primes?
541,341.