Prime numbers between 8301 and 8,400
There are 9 prime numbers between 8301 and 8,400: 8311, 8317, 8329, 8353, 8363, 8369, 8377, 8387, 8389.
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 ā8400 ā 91.7 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 9 primes between 8301 and 8,400, with a total of 75,195.
- 3
The biggest gap between neighbouring primes in this range is 24, after 8329 (the next prime is 8353). There are 1 twin prime pairs (primes 2 apart): (8387, 8389).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 8,301 to 8,310 | 0 | 0% |
| 8,311 to 8,320 | 2 | 20% |
| 8,321 to 8,330 | 1 | 10% |
| 8,331 to 8,340 | 0 | 0% |
| 8,341 to 8,350 | 0 | 0% |
| 8,351 to 8,360 | 1 | 10% |
| 8,361 to 8,370 | 2 | 20% |
| 8,371 to 8,380 | 1 | 10% |
| 8,381 to 8,390 | 2 | 20% |
| 8,391 to 8,400 | 0 | 0% |
Questions
How many prime numbers are there between 8301 and 8,400?
9.
What is the biggest prime number below 8,400?
8389.
What is the first prime number after 8300?
8311.