Prime numbers between 8601 and 8,700
There are 13 prime numbers between 8601 and 8,700: 8609, 8623, 8627, 8629, 8641, 8647, 8663, 8669, 8677, 8681, 8689, 8693, 8699.
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 ā8700 ā 93.3 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 13 primes between 8601 and 8,700, with a total of 112,547.
- 3
The biggest gap between neighbouring primes in this range is 16, after 8647 (the next prime is 8663). There are 1 twin prime pairs (primes 2 apart): (8627, 8629).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 8,601 to 8,610 | 1 | 10% |
| 8,611 to 8,620 | 0 | 0% |
| 8,621 to 8,630 | 3 | 30% |
| 8,631 to 8,640 | 0 | 0% |
| 8,641 to 8,650 | 2 | 20% |
| 8,651 to 8,660 | 0 | 0% |
| 8,661 to 8,670 | 2 | 20% |
| 8,671 to 8,680 | 1 | 10% |
| 8,681 to 8,690 | 2 | 20% |
| 8,691 to 8,700 | 2 | 20% |
Questions
How many prime numbers are there between 8601 and 8,700?
13.
What is the biggest prime number below 8,700?
8699.
What is the first prime number after 8600?
8609.