Prime numbers between 5001 and 5,100
There are 12 prime numbers between 5001 and 5,100: 5003, 5009, 5011, 5021, 5023, 5039, 5051, 5059, 5077, 5081, 5087, 5099.
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 ā5100 ā 71.4 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 12 primes between 5001 and 5,100, with a total of 60,560.
- 3
The biggest gap between neighbouring primes in this range is 18, after 5059 (the next prime is 5077). There are 2 twin prime pairs (primes 2 apart): (5009, 5011), (5021, 5023).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 5,001 to 5,010 | 2 | 20% |
| 5,011 to 5,020 | 1 | 10% |
| 5,021 to 5,030 | 2 | 20% |
| 5,031 to 5,040 | 1 | 10% |
| 5,041 to 5,050 | 0 | 0% |
| 5,051 to 5,060 | 2 | 20% |
| 5,061 to 5,070 | 0 | 0% |
| 5,071 to 5,080 | 1 | 10% |
| 5,081 to 5,090 | 2 | 20% |
| 5,091 to 5,100 | 1 | 10% |
Questions
How many prime numbers are there between 5001 and 5,100?
12.
What is the biggest prime number below 5,100?
5099.
What is the first prime number after 5000?
5003.