Prime numbers between 8701 and 8,800
There are 11 prime numbers between 8701 and 8,800: 8707, 8713, 8719, 8731, 8737, 8741, 8747, 8753, 8761, 8779, 8783.
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 ā8800 ā 93.8 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 11 primes between 8701 and 8,800, with a total of 96,171.
- 3
The biggest gap between neighbouring primes in this range is 18, after 8761 (the next prime is 8779). There are no twin primes here.
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 8,701 to 8,710 | 1 | 10% |
| 8,711 to 8,720 | 2 | 20% |
| 8,721 to 8,730 | 0 | 0% |
| 8,731 to 8,740 | 2 | 20% |
| 8,741 to 8,750 | 2 | 20% |
| 8,751 to 8,760 | 1 | 10% |
| 8,761 to 8,770 | 1 | 10% |
| 8,771 to 8,780 | 1 | 10% |
| 8,781 to 8,790 | 1 | 10% |
| 8,791 to 8,800 | 0 | 0% |
Questions
How many prime numbers are there between 8701 and 8,800?
11.
What is the biggest prime number below 8,800?
8783.
What is the first prime number after 8700?
8707.