Prime numbers between 7401 and 7,500
There are 11 prime numbers between 7401 and 7,500: 7411, 7417, 7433, 7451, 7457, 7459, 7477, 7481, 7487, 7489, 7499.
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 ā7500 ā 86.6 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 11 primes between 7401 and 7,500, with a total of 82,061.
- 3
The biggest gap between neighbouring primes in this range is 18, after 7433 (the next prime is 7451). There are 2 twin prime pairs (primes 2 apart): (7457, 7459), (7487, 7489).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 7,401 to 7,410 | 0 | 0% |
| 7,411 to 7,420 | 2 | 20% |
| 7,421 to 7,430 | 0 | 0% |
| 7,431 to 7,440 | 1 | 10% |
| 7,441 to 7,450 | 0 | 0% |
| 7,451 to 7,460 | 3 | 30% |
| 7,461 to 7,470 | 0 | 0% |
| 7,471 to 7,480 | 1 | 10% |
| 7,481 to 7,490 | 3 | 30% |
| 7,491 to 7,500 | 1 | 10% |
Questions
How many prime numbers are there between 7401 and 7,500?
11.
What is the biggest prime number below 7,500?
7499.
What is the first prime number after 7400?
7411.