Prime numbers between 2301 and 2,400
There are 15 prime numbers between 2301 and 2,400: 2309, 2311, 2333, 2339, 2341, 2347, 2351, 2357, 2371, 2377, 2381, 2383, 2389, 2393, 2399.
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 ā2400 ā 49.0 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 15 primes between 2301 and 2,400, with a total of 35,381.
- 3
The biggest gap between neighbouring primes in this range is 22, after 2311 (the next prime is 2333). There are 3 twin prime pairs (primes 2 apart): (2309, 2311), (2339, 2341), (2381, 2383).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 2,301 to 2,310 | 1 | 10% |
| 2,311 to 2,320 | 1 | 10% |
| 2,321 to 2,330 | 0 | 0% |
| 2,331 to 2,340 | 2 | 20% |
| 2,341 to 2,350 | 2 | 20% |
| 2,351 to 2,360 | 2 | 20% |
| 2,361 to 2,370 | 0 | 0% |
| 2,371 to 2,380 | 2 | 20% |
| 2,381 to 2,390 | 3 | 30% |
| 2,391 to 2,400 | 2 | 20% |
Questions
How many prime numbers are there between 2301 and 2,400?
15.
What is the biggest prime number below 2,400?
2399.
What is the first prime number after 2300?
2309.