What is the 6401st prime number?
The 6401st prime number is 63823. The next prime is 63839 (a gap of 16) and the one before is 63809.
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 6401st one is 63823.
- 2
63823 is prime because no prime up to ā63823 ā 252.63 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 6401st prime is close to 6401 Ć ln(6401) ā 56100, and here it is 63823.
- 4
63823 has no twin: neither 63821 nor 63825 is prime.
Primes around the 6401st
| Position | Prime | Gap from the previous |
|---|---|---|
| 6398 | 63799 | 6 |
| 6399 | 63803 | 4 |
| 6400 | 63809 | 6 |
| 6401 | 63823 | 14 |
| 6402 | 63839 | 16 |
| 6403 | 63841 | 2 |
| 6404 | 63853 | 12 |
Questions
What is the 6401st prime number?
63823.
Which prime number is 63823?
63823 is the 6401st prime number.
What is the sum of the first 6401 primes?
193,164,298.