Prime numbers between 8501 and 8,600
There are 12 prime numbers between 8501 and 8,600: 8501, 8513, 8521, 8527, 8537, 8539, 8543, 8563, 8573, 8581, 8597, 8599.
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 ā8600 ā 92.7 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 12 primes between 8501 and 8,600, with a total of 102,594.
- 3
The biggest gap between neighbouring primes in this range is 20, after 8543 (the next prime is 8563). There are 2 twin prime pairs (primes 2 apart): (8537, 8539), (8597, 8599).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 8,501 to 8,510 | 1 | 10% |
| 8,511 to 8,520 | 1 | 10% |
| 8,521 to 8,530 | 2 | 20% |
| 8,531 to 8,540 | 2 | 20% |
| 8,541 to 8,550 | 1 | 10% |
| 8,551 to 8,560 | 0 | 0% |
| 8,561 to 8,570 | 1 | 10% |
| 8,571 to 8,580 | 1 | 10% |
| 8,581 to 8,590 | 1 | 10% |
| 8,591 to 8,600 | 2 | 20% |
Questions
How many prime numbers are there between 8501 and 8,600?
12.
What is the biggest prime number below 8,600?
8599.
What is the first prime number after 8500?
8501.