Prime numbers between 9801 and 9,900
There are 12 prime numbers between 9801 and 9,900: 9803, 9811, 9817, 9829, 9833, 9839, 9851, 9857, 9859, 9871, 9883, 9887.
How to work it out
- 1
A prime has exactly two factors, 1 and itself. To list them, cross out multiples of 2, then 3, then 5, and so on up to ā9900 ā 99.5 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 12 primes between 9801 and 9,900, with a total of 118,140.
- 3
The biggest gap between neighbouring primes in this range is 12, after 9817 (the next prime is 9829). There are 1 twin prime pairs (primes 2 apart): (9857, 9859).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 9,801 to 9,810 | 1 | 10% |
| 9,811 to 9,820 | 2 | 20% |
| 9,821 to 9,830 | 1 | 10% |
| 9,831 to 9,840 | 2 | 20% |
| 9,841 to 9,850 | 0 | 0% |
| 9,851 to 9,860 | 3 | 30% |
| 9,861 to 9,870 | 0 | 0% |
| 9,871 to 9,880 | 1 | 10% |
| 9,881 to 9,890 | 2 | 20% |
| 9,891 to 9,900 | 0 | 0% |
Questions
How many prime numbers are there between 9801 and 9,900?
12.
What is the biggest prime number below 9,900?
9887.
What is the first prime number after 9800?
9803.