What is the 446th prime number?
The 446th prime number is 3137. The next prime is 3163 (a gap of 26) and the one before is 3121.
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 446th one is 3137.
- 2
3137 is prime because no prime up to ā3137 ā 56.01 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 446th prime is close to 446 Ć ln(446) ā 2721, and here it is 3137.
- 4
3137 has no twin: neither 3135 nor 3139 is prime.
Primes around the 446th
| Position | Prime | Gap from the previous |
|---|---|---|
| 443 | 3109 | 20 |
| 444 | 3119 | 10 |
| 445 | 3121 | 2 |
| 446 | 3137 | 16 |
| 447 | 3163 | 26 |
| 448 | 3167 | 4 |
| 449 | 3169 | 2 |
Questions
What is the 446th prime number?
3137.
Which prime number is 3137?
3137 is the 446th prime number.
What is the sum of the first 446 primes?
642,869.