Prime numbers between 4501 and 4,600
There are 12 prime numbers between 4501 and 4,600: 4507, 4513, 4517, 4519, 4523, 4547, 4549, 4561, 4567, 4583, 4591, 4597.
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 ā4600 ā 67.8 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 12 primes between 4501 and 4,600, with a total of 54,574.
- 3
The biggest gap between neighbouring primes in this range is 24, after 4523 (the next prime is 4547). There are 2 twin prime pairs (primes 2 apart): (4517, 4519), (4547, 4549).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 4,501 to 4,510 | 1 | 10% |
| 4,511 to 4,520 | 3 | 30% |
| 4,521 to 4,530 | 1 | 10% |
| 4,531 to 4,540 | 0 | 0% |
| 4,541 to 4,550 | 2 | 20% |
| 4,551 to 4,560 | 0 | 0% |
| 4,561 to 4,570 | 2 | 20% |
| 4,571 to 4,580 | 0 | 0% |
| 4,581 to 4,590 | 1 | 10% |
| 4,591 to 4,600 | 2 | 20% |
Questions
How many prime numbers are there between 4501 and 4,600?
12.
What is the biggest prime number below 4,600?
4597.
What is the first prime number after 4500?
4507.