Prime numbers between 9901 and 10,000
There are 9 prime numbers between 9901 and 10,000: 9901, 9907, 9923, 9929, 9931, 9941, 9949, 9967, 9973.
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 ā10000 ā 100.0 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 9 primes between 9901 and 10,000, with a total of 89,421.
- 3
The biggest gap between neighbouring primes in this range is 18, after 9949 (the next prime is 9967). There are 1 twin prime pairs (primes 2 apart): (9929, 9931).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 9,901 to 9,910 | 2 | 20% |
| 9,911 to 9,920 | 0 | 0% |
| 9,921 to 9,930 | 2 | 20% |
| 9,931 to 9,940 | 1 | 10% |
| 9,941 to 9,950 | 2 | 20% |
| 9,951 to 9,960 | 0 | 0% |
| 9,961 to 9,970 | 1 | 10% |
| 9,971 to 9,980 | 1 | 10% |
| 9,981 to 9,990 | 0 | 0% |
| 9,991 to 10,000 | 0 | 0% |
Questions
How many prime numbers are there between 9901 and 10,000?
9.
What is the biggest prime number below 10,000?
9973.
What is the first prime number after 9900?
9901.