Prime numbers between 7501 and 7,600
There are 15 prime numbers between 7501 and 7,600: 7507, 7517, 7523, 7529, 7537, 7541, 7547, 7549, 7559, 7561, 7573, 7577, 7583, 7589, 7591.
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 ā7600 ā 87.2 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 15 primes between 7501 and 7,600, with a total of 113,283.
- 3
The biggest gap between neighbouring primes in this range is 12, after 7561 (the next prime is 7573). There are 3 twin prime pairs (primes 2 apart): (7547, 7549), (7559, 7561), (7589, 7591).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 7,501 to 7,510 | 1 | 10% |
| 7,511 to 7,520 | 1 | 10% |
| 7,521 to 7,530 | 2 | 20% |
| 7,531 to 7,540 | 1 | 10% |
| 7,541 to 7,550 | 3 | 30% |
| 7,551 to 7,560 | 1 | 10% |
| 7,561 to 7,570 | 1 | 10% |
| 7,571 to 7,580 | 2 | 20% |
| 7,581 to 7,590 | 2 | 20% |
| 7,591 to 7,600 | 1 | 10% |
Questions
How many prime numbers are there between 7501 and 7,600?
15.
What is the biggest prime number below 7,600?
7591.
What is the first prime number after 7500?
7507.