Prime numbers between 5301 and 5,400
There are 10 prime numbers between 5301 and 5,400: 5303, 5309, 5323, 5333, 5347, 5351, 5381, 5387, 5393, 5399.
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 ā5400 ā 73.5 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 10 primes between 5301 and 5,400, with a total of 53,526.
- 3
The biggest gap between neighbouring primes in this range is 30, after 5351 (the next prime is 5381). There are no twin primes here.
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 5,301 to 5,310 | 2 | 20% |
| 5,311 to 5,320 | 0 | 0% |
| 5,321 to 5,330 | 1 | 10% |
| 5,331 to 5,340 | 1 | 10% |
| 5,341 to 5,350 | 1 | 10% |
| 5,351 to 5,360 | 1 | 10% |
| 5,361 to 5,370 | 0 | 0% |
| 5,371 to 5,380 | 0 | 0% |
| 5,381 to 5,390 | 2 | 20% |
| 5,391 to 5,400 | 2 | 20% |
Questions
How many prime numbers are there between 5301 and 5,400?
10.
What is the biggest prime number below 5,400?
5399.
What is the first prime number after 5300?
5303.