What is the 9642nd prime number?
The 9642nd prime number is 100591. The next prime is 100609 (a gap of 18) and the one before is 100559.
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 9642nd one is 100591.
- 2
100591 is prime because no prime up to ā100591 ā 317.16 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 9642nd prime is close to 9642 Ć ln(9642) ā 88455, and here it is 100591.
- 4
100591 has no twin: neither 100589 nor 100593 is prime.
Primes around the 9642nd
| Position | Prime | Gap from the previous |
|---|---|---|
| 9639 | 100547 | 10 |
| 9640 | 100549 | 2 |
| 9641 | 100559 | 10 |
| 9642 | 100591 | 32 |
| 9643 | 100609 | 18 |
| 9644 | 100613 | 4 |
| 9645 | 100621 | 8 |
Questions
What is the 9642nd prime number?
100591.
Which prime number is 100591?
100591 is the 9642nd prime number.
What is the sum of the first 9642 primes?
459,412,387.