What is the 8638th prime number?
The 8638th prime number is 89189. The next prime is 89203 (a gap of 14) and the one before is 89153.
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 8638th one is 89189.
- 2
89189 is prime because no prime up to ā89189 ā 298.65 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 8638th prime is close to 8638 Ć ln(8638) ā 78294, and here it is 89189.
- 4
89189 has no twin: neither 89187 nor 89191 is prime.
Primes around the 8638th
| Position | Prime | Gap from the previous |
|---|---|---|
| 8635 | 89123 | 4 |
| 8636 | 89137 | 14 |
| 8637 | 89153 | 16 |
| 8638 | 89189 | 36 |
| 8639 | 89203 | 14 |
| 8640 | 89209 | 6 |
| 8641 | 89213 | 4 |
Questions
What is the 8638th prime number?
89189.
Which prime number is 89189?
89189 is the 8638th prime number.
What is the sum of the first 8638 primes?
364,207,609.