Prime numbers between 5701 and 5,800
There are 10 prime numbers between 5701 and 5,800: 5701, 5711, 5717, 5737, 5741, 5743, 5749, 5779, 5783, 5791.
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 ā5800 ā 76.2 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 10 primes between 5701 and 5,800, with a total of 57,452.
- 3
The biggest gap between neighbouring primes in this range is 30, after 5749 (the next prime is 5779). There are 1 twin prime pairs (primes 2 apart): (5741, 5743).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 5,701 to 5,710 | 1 | 10% |
| 5,711 to 5,720 | 2 | 20% |
| 5,721 to 5,730 | 0 | 0% |
| 5,731 to 5,740 | 1 | 10% |
| 5,741 to 5,750 | 3 | 30% |
| 5,751 to 5,760 | 0 | 0% |
| 5,761 to 5,770 | 0 | 0% |
| 5,771 to 5,780 | 1 | 10% |
| 5,781 to 5,790 | 1 | 10% |
| 5,791 to 5,800 | 1 | 10% |
Questions
How many prime numbers are there between 5701 and 5,800?
10.
What is the biggest prime number below 5,800?
5791.
What is the first prime number after 5700?
5701.