Prime numbers between 4901 and 5,000
There are 15 prime numbers between 4901 and 5,000: 4903, 4909, 4919, 4931, 4933, 4937, 4943, 4951, 4957, 4967, 4969, 4973, 4987, 4993, 4999.
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 ā5000 ā 70.7 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 15 primes between 4901 and 5,000, with a total of 74,271.
- 3
The biggest gap between neighbouring primes in this range is 14, after 4973 (the next prime is 4987). There are 2 twin prime pairs (primes 2 apart): (4931, 4933), (4967, 4969).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 4,901 to 4,910 | 2 | 20% |
| 4,911 to 4,920 | 1 | 10% |
| 4,921 to 4,930 | 0 | 0% |
| 4,931 to 4,940 | 3 | 30% |
| 4,941 to 4,950 | 1 | 10% |
| 4,951 to 4,960 | 2 | 20% |
| 4,961 to 4,970 | 2 | 20% |
| 4,971 to 4,980 | 1 | 10% |
| 4,981 to 4,990 | 1 | 10% |
| 4,991 to 5,000 | 2 | 20% |
Questions
How many prime numbers are there between 4901 and 5,000?
15.
What is the biggest prime number below 5,000?
4999.
What is the first prime number after 4900?
4903.