Prime numbers between 4701 and 4,800
There are 12 prime numbers between 4701 and 4,800: 4703, 4721, 4723, 4729, 4733, 4751, 4759, 4783, 4787, 4789, 4793, 4799.
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 ā4800 ā 69.3 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 12 primes between 4701 and 4,800, with a total of 57,070.
- 3
The biggest gap between neighbouring primes in this range is 24, after 4759 (the next prime is 4783). There are 2 twin prime pairs (primes 2 apart): (4721, 4723), (4787, 4789).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 4,701 to 4,710 | 1 | 10% |
| 4,711 to 4,720 | 0 | 0% |
| 4,721 to 4,730 | 3 | 30% |
| 4,731 to 4,740 | 1 | 10% |
| 4,741 to 4,750 | 0 | 0% |
| 4,751 to 4,760 | 2 | 20% |
| 4,761 to 4,770 | 0 | 0% |
| 4,771 to 4,780 | 0 | 0% |
| 4,781 to 4,790 | 3 | 30% |
| 4,791 to 4,800 | 2 | 20% |
Questions
How many prime numbers are there between 4701 and 4,800?
12.
What is the biggest prime number below 4,800?
4799.
What is the first prime number after 4700?
4703.