Prime numbers between 9401 and 9,500
There are 15 prime numbers between 9401 and 9,500: 9403, 9413, 9419, 9421, 9431, 9433, 9437, 9439, 9461, 9463, 9467, 9473, 9479, 9491, 9497.
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 ā9500 ā 97.5 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 15 primes between 9401 and 9,500, with a total of 141,727.
- 3
The biggest gap between neighbouring primes in this range is 22, after 9439 (the next prime is 9461). There are 4 twin prime pairs (primes 2 apart): (9419, 9421), (9431, 9433), (9437, 9439), (9461, 9463).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 9,401 to 9,410 | 1 | 10% |
| 9,411 to 9,420 | 2 | 20% |
| 9,421 to 9,430 | 1 | 10% |
| 9,431 to 9,440 | 4 | 40% |
| 9,441 to 9,450 | 0 | 0% |
| 9,451 to 9,460 | 0 | 0% |
| 9,461 to 9,470 | 3 | 30% |
| 9,471 to 9,480 | 2 | 20% |
| 9,481 to 9,490 | 0 | 0% |
| 9,491 to 9,500 | 2 | 20% |
Questions
How many prime numbers are there between 9401 and 9,500?
15.
What is the biggest prime number below 9,500?
9497.
What is the first prime number after 9400?
9403.