Prime numbers between 8401 and 8,500
There are 8 prime numbers between 8401 and 8,500: 8419, 8423, 8429, 8431, 8443, 8447, 8461, 8467.
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 ā8500 ā 92.2 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 8 primes between 8401 and 8,500, with a total of 67,520.
- 3
The biggest gap between neighbouring primes in this range is 14, after 8447 (the next prime is 8461). There are 1 twin prime pairs (primes 2 apart): (8429, 8431).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 8,401 to 8,410 | 0 | 0% |
| 8,411 to 8,420 | 1 | 10% |
| 8,421 to 8,430 | 2 | 20% |
| 8,431 to 8,440 | 1 | 10% |
| 8,441 to 8,450 | 2 | 20% |
| 8,451 to 8,460 | 0 | 0% |
| 8,461 to 8,470 | 2 | 20% |
| 8,471 to 8,480 | 0 | 0% |
| 8,481 to 8,490 | 0 | 0% |
| 8,491 to 8,500 | 0 | 0% |
Questions
How many prime numbers are there between 8401 and 8,500?
8.
What is the biggest prime number below 8,500?
8467.
What is the first prime number after 8400?
8419.