Prime numbers between 5601 and 5,700
There are 12 prime numbers between 5601 and 5,700: 5623, 5639, 5641, 5647, 5651, 5653, 5657, 5659, 5669, 5683, 5689, 5693.
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 ā5700 ā 75.5 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 12 primes between 5601 and 5,700, with a total of 67,904.
- 3
The biggest gap between neighbouring primes in this range is 16, after 5623 (the next prime is 5639). There are 3 twin prime pairs (primes 2 apart): (5639, 5641), (5651, 5653), (5657, 5659).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 5,601 to 5,610 | 0 | 0% |
| 5,611 to 5,620 | 0 | 0% |
| 5,621 to 5,630 | 1 | 10% |
| 5,631 to 5,640 | 1 | 10% |
| 5,641 to 5,650 | 2 | 20% |
| 5,651 to 5,660 | 4 | 40% |
| 5,661 to 5,670 | 1 | 10% |
| 5,671 to 5,680 | 0 | 0% |
| 5,681 to 5,690 | 2 | 20% |
| 5,691 to 5,700 | 1 | 10% |
Questions
How many prime numbers are there between 5601 and 5,700?
12.
What is the biggest prime number below 5,700?
5693.
What is the first prime number after 5600?
5623.