What is the 8401st prime number?
The 8401st prime number is 86381. The next prime is 86389 (a gap of 8) and the one before is 86371.
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 8401st one is 86381.
- 2
86381 is prime because no prime up to ā86381 ā 293.91 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 8401st prime is close to 8401 Ć ln(8401) ā 75912, and here it is 86381.
- 4
86381 has no twin: neither 86379 nor 86383 is prime.
Primes around the 8401st
| Position | Prime | Gap from the previous |
|---|---|---|
| 8398 | 86357 | 4 |
| 8399 | 86369 | 12 |
| 8400 | 86371 | 2 |
| 8401 | 86381 | 10 |
| 8402 | 86389 | 8 |
| 8403 | 86399 | 10 |
| 8404 | 86413 | 14 |
Questions
What is the 8401st prime number?
86381.
Which prime number is 86381?
86381 is the 8401st prime number.
What is the sum of the first 8401 primes?
343,399,970.