What is the 4096th prime number?
The 4096th prime number is 38873. The next prime is 38891 (a gap of 18) and the one before is 38867.
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 4096th one is 38873.
- 2
38873 is prime because no prime up to ā38873 ā 197.16 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 4096th prime is close to 4096 Ć ln(4096) ā 34070, and here it is 38873.
- 4
38873 has no twin: neither 38871 nor 38875 is prime.
Primes around the 4096th
| Position | Prime | Gap from the previous |
|---|---|---|
| 4093 | 38851 | 12 |
| 4094 | 38861 | 10 |
| 4095 | 38867 | 6 |
| 4096 | 38873 | 6 |
| 4097 | 38891 | 18 |
| 4098 | 38903 | 12 |
| 4099 | 38917 | 14 |
Questions
What is the 4096th prime number?
38873.
Which prime number is 38873?
38873 is the 4096th prime number.
What is the sum of the first 4096 primes?
74,950,547.