What is the 442nd prime number?
The 442nd prime number is 3089. The next prime is 3109 (a gap of 20) and the one before is 3083.
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 442nd one is 3089.
- 2
3089 is prime because no prime up to ā3089 ā 55.58 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 442nd prime is close to 442 Ć ln(442) ā 2692, and here it is 3089.
- 4
3089 has no twin: neither 3087 nor 3091 is prime.
Primes around the 442nd
| Position | Prime | Gap from the previous |
|---|---|---|
| 439 | 3067 | 6 |
| 440 | 3079 | 12 |
| 441 | 3083 | 4 |
| 442 | 3089 | 6 |
| 443 | 3109 | 20 |
| 444 | 3119 | 10 |
| 445 | 3121 | 2 |
Questions
What is the 442nd prime number?
3089.
Which prime number is 3089?
3089 is the 442nd prime number.
What is the sum of the first 442 primes?
630,383.