Prime numbers between 2201 and 2,300
There are 15 prime numbers between 2201 and 2,300: 2203, 2207, 2213, 2221, 2237, 2239, 2243, 2251, 2267, 2269, 2273, 2281, 2287, 2293, 2297.
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 ā2300 ā 48.0 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 15 primes between 2201 and 2,300, with a total of 33,781.
- 3
The biggest gap between neighbouring primes in this range is 16, after 2221 (the next prime is 2237). There are 2 twin prime pairs (primes 2 apart): (2237, 2239), (2267, 2269).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 2,201 to 2,210 | 2 | 20% |
| 2,211 to 2,220 | 1 | 10% |
| 2,221 to 2,230 | 1 | 10% |
| 2,231 to 2,240 | 2 | 20% |
| 2,241 to 2,250 | 1 | 10% |
| 2,251 to 2,260 | 1 | 10% |
| 2,261 to 2,270 | 2 | 20% |
| 2,271 to 2,280 | 1 | 10% |
| 2,281 to 2,290 | 2 | 20% |
| 2,291 to 2,300 | 2 | 20% |
Questions
How many prime numbers are there between 2201 and 2,300?
15.
What is the biggest prime number below 2,300?
2297.
What is the first prime number after 2200?
2203.