What is the 8400th prime number?
The 8400th prime number is 86371. The next prime is 86381 (a gap of 10) and the one before is 86369.
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 8400th one is 86371.
- 2
86371 is prime because no prime up to ā86371 ā 293.89 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 8400th prime is close to 8400 Ć ln(8400) ā 75902, and here it is 86371.
- 4
86371 is a twin prime: 86369 and 86371 are both prime.
Primes around the 8400th
| Position | Prime | Gap from the previous |
|---|---|---|
| 8397 | 86353 | 2 |
| 8398 | 86357 | 4 |
| 8399 | 86369 | 12 |
| 8400 | 86371 | 2 |
| 8401 | 86381 | 10 |
| 8402 | 86389 | 8 |
| 8403 | 86399 | 10 |
Questions
What is the 8400th prime number?
86371.
Which prime number is 86371?
86371 is the 8400th prime number.
What is the sum of the first 8400 primes?
343,313,589.