What is the 4100th prime number?
The 4100th prime number is 38921. The next prime is 38923 (a gap of 2) and the one before is 38917.
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 4100th one is 38921.
- 2
38921 is prime because no prime up to ā38921 ā 197.28 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 4100th prime is close to 4100 Ć ln(4100) ā 34107, and here it is 38921.
- 4
38921 is a twin prime: 38921 and 38923 are both prime.
Primes around the 4100th
| Position | Prime | Gap from the previous |
|---|---|---|
| 4097 | 38891 | 18 |
| 4098 | 38903 | 12 |
| 4099 | 38917 | 14 |
| 4100 | 38921 | 4 |
| 4101 | 38923 | 2 |
| 4102 | 38933 | 10 |
| 4103 | 38953 | 20 |
Questions
What is the 4100th prime number?
38921.
Which prime number is 38921?
38921 is the 4100th prime number.
What is the sum of the first 4100 primes?
75,106,179.