What is the 9600th prime number?
The 9600th prime number is 100109. The next prime is 100129 (a gap of 20) and the one before is 100103.
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 9600th one is 100109.
- 2
100109 is prime because no prime up to ā100109 ā 316.40 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 9600th prime is close to 9600 Ć ln(9600) ā 88027, and here it is 100109.
- 4
100109 has no twin: neither 100107 nor 100111 is prime.
Primes around the 9600th
| Position | Prime | Gap from the previous |
|---|---|---|
| 9597 | 100057 | 8 |
| 9598 | 100069 | 12 |
| 9599 | 100103 | 34 |
| 9600 | 100109 | 6 |
| 9601 | 100129 | 20 |
| 9602 | 100151 | 22 |
| 9603 | 100153 | 2 |
Questions
What is the 9600th prime number?
100109.
Which prime number is 100109?
100109 is the 9600th prime number.
What is the sum of the first 9600 primes?
455,196,989.