What is the 2100th prime number?
The 2100th prime number is 18313. The next prime is 18329 (a gap of 16) and the one before is 18311.
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 2100th one is 18313.
- 2
18313 is prime because no prime up to ā18313 ā 135.33 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 2100th prime is close to 2100 Ć ln(2100) ā 16064, and here it is 18313.
- 4
18313 is a twin prime: 18311 and 18313 are both prime.
Primes around the 2100th
| Position | Prime | Gap from the previous |
|---|---|---|
| 2097 | 18301 | 12 |
| 2098 | 18307 | 6 |
| 2099 | 18311 | 4 |
| 2100 | 18313 | 2 |
| 2101 | 18329 | 16 |
| 2102 | 18341 | 12 |
| 2103 | 18353 | 12 |
Questions
What is the 2100th prime number?
18313.
Which prime number is 18313?
18313 is the 2100th prime number.
What is the sum of the first 2100 primes?
18,061,527.