What is the 438th prime number?
The 438th prime number is 3061. The next prime is 3067 (a gap of 6) and the one before is 3049.
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 438th one is 3061.
- 2
3061 is prime because no prime up to ā3061 ā 55.33 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 438th prime is close to 438 Ć ln(438) ā 2664, and here it is 3061.
- 4
3061 has no twin: neither 3059 nor 3063 is prime.
Primes around the 438th
| Position | Prime | Gap from the previous |
|---|---|---|
| 435 | 3037 | 14 |
| 436 | 3041 | 4 |
| 437 | 3049 | 8 |
| 438 | 3061 | 12 |
| 439 | 3067 | 6 |
| 440 | 3079 | 12 |
| 441 | 3083 | 4 |
Questions
What is the 438th prime number?
3061.
Which prime number is 3061?
3061 is the 438th prime number.
What is the sum of the first 438 primes?
618,065.