What is the 4097th prime number?
The 4097th prime number is 38891. The next prime is 38903 (a gap of 12) and the one before is 38873.
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 4097th one is 38891.
- 2
38891 is prime because no prime up to ā38891 ā 197.21 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 4097th prime is close to 4097 Ć ln(4097) ā 34079, and here it is 38891.
- 4
38891 has no twin: neither 38889 nor 38893 is prime.
Primes around the 4097th
| Position | Prime | Gap from the previous |
|---|---|---|
| 4094 | 38861 | 10 |
| 4095 | 38867 | 6 |
| 4096 | 38873 | 6 |
| 4097 | 38891 | 18 |
| 4098 | 38903 | 12 |
| 4099 | 38917 | 14 |
| 4100 | 38921 | 4 |
Questions
What is the 4097th prime number?
38891.
Which prime number is 38891?
38891 is the 4097th prime number.
What is the sum of the first 4097 primes?
74,989,438.