Prime numbers between 2401 and 2,500
There are 10 prime numbers between 2401 and 2,500: 2411, 2417, 2423, 2437, 2441, 2447, 2459, 2467, 2473, 2477.
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 ā2500 ā 50.0 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 10 primes between 2401 and 2,500, with a total of 24,452.
- 3
The biggest gap between neighbouring primes in this range is 14, after 2423 (the next prime is 2437). There are no twin primes here.
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 2,401 to 2,410 | 0 | 0% |
| 2,411 to 2,420 | 2 | 20% |
| 2,421 to 2,430 | 1 | 10% |
| 2,431 to 2,440 | 1 | 10% |
| 2,441 to 2,450 | 2 | 20% |
| 2,451 to 2,460 | 1 | 10% |
| 2,461 to 2,470 | 1 | 10% |
| 2,471 to 2,480 | 2 | 20% |
| 2,481 to 2,490 | 0 | 0% |
| 2,491 to 2,500 | 0 | 0% |
Questions
How many prime numbers are there between 2401 and 2,500?
10.
What is the biggest prime number below 2,500?
2477.
What is the first prime number after 2400?
2411.