Prime numbers between 9701 and 9,800
There are 11 prime numbers between 9701 and 9,800: 9719, 9721, 9733, 9739, 9743, 9749, 9767, 9769, 9781, 9787, 9791.
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 ā9800 ā 99.0 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 11 primes between 9701 and 9,800, with a total of 107,299.
- 3
The biggest gap between neighbouring primes in this range is 18, after 9749 (the next prime is 9767). There are 2 twin prime pairs (primes 2 apart): (9719, 9721), (9767, 9769).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 9,701 to 9,710 | 0 | 0% |
| 9,711 to 9,720 | 1 | 10% |
| 9,721 to 9,730 | 1 | 10% |
| 9,731 to 9,740 | 2 | 20% |
| 9,741 to 9,750 | 2 | 20% |
| 9,751 to 9,760 | 0 | 0% |
| 9,761 to 9,770 | 2 | 20% |
| 9,771 to 9,780 | 0 | 0% |
| 9,781 to 9,790 | 2 | 20% |
| 9,791 to 9,800 | 1 | 10% |
Questions
How many prime numbers are there between 9701 and 9,800?
11.
What is the biggest prime number below 9,800?
9791.
What is the first prime number after 9700?
9719.