Prime numbers between 5101 and 5,200
There are 11 prime numbers between 5101 and 5,200: 5101, 5107, 5113, 5119, 5147, 5153, 5167, 5171, 5179, 5189, 5197.
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 ā5200 ā 72.1 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 11 primes between 5101 and 5,200, with a total of 56,643.
- 3
The biggest gap between neighbouring primes in this range is 28, after 5119 (the next prime is 5147). There are no twin primes here.
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 5,101 to 5,110 | 2 | 20% |
| 5,111 to 5,120 | 2 | 20% |
| 5,121 to 5,130 | 0 | 0% |
| 5,131 to 5,140 | 0 | 0% |
| 5,141 to 5,150 | 1 | 10% |
| 5,151 to 5,160 | 1 | 10% |
| 5,161 to 5,170 | 1 | 10% |
| 5,171 to 5,180 | 2 | 20% |
| 5,181 to 5,190 | 1 | 10% |
| 5,191 to 5,200 | 1 | 10% |
Questions
How many prime numbers are there between 5101 and 5,200?
11.
What is the biggest prime number below 5,200?
5197.
What is the first prime number after 5100?
5101.