Prime numbers between 8201 and 8,300
There are 14 prime numbers between 8201 and 8,300: 8209, 8219, 8221, 8231, 8233, 8237, 8243, 8263, 8269, 8273, 8287, 8291, 8293, 8297.
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 ā8300 ā 91.1 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 14 primes between 8201 and 8,300, with a total of 115,566.
- 3
The biggest gap between neighbouring primes in this range is 20, after 8243 (the next prime is 8263). There are 3 twin prime pairs (primes 2 apart): (8219, 8221), (8231, 8233), (8291, 8293).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 8,201 to 8,210 | 1 | 10% |
| 8,211 to 8,220 | 1 | 10% |
| 8,221 to 8,230 | 1 | 10% |
| 8,231 to 8,240 | 3 | 30% |
| 8,241 to 8,250 | 1 | 10% |
| 8,251 to 8,260 | 0 | 0% |
| 8,261 to 8,270 | 2 | 20% |
| 8,271 to 8,280 | 1 | 10% |
| 8,281 to 8,290 | 1 | 10% |
| 8,291 to 8,300 | 3 | 30% |
Questions
How many prime numbers are there between 8201 and 8,300?
14.
What is the biggest prime number below 8,300?
8297.
What is the first prime number after 8200?
8209.