Prime numbers between 7901 and 8,000
There are 10 prime numbers between 7901 and 8,000: 7901, 7907, 7919, 7927, 7933, 7937, 7949, 7951, 7963, 7993.
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 ā8000 ā 89.4 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 10 primes between 7901 and 8,000, with a total of 79,380.
- 3
The biggest gap between neighbouring primes in this range is 30, after 7963 (the next prime is 7993). There are 1 twin prime pairs (primes 2 apart): (7949, 7951).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 7,901 to 7,910 | 2 | 20% |
| 7,911 to 7,920 | 1 | 10% |
| 7,921 to 7,930 | 1 | 10% |
| 7,931 to 7,940 | 2 | 20% |
| 7,941 to 7,950 | 1 | 10% |
| 7,951 to 7,960 | 1 | 10% |
| 7,961 to 7,970 | 1 | 10% |
| 7,971 to 7,980 | 0 | 0% |
| 7,981 to 7,990 | 0 | 0% |
| 7,991 to 8,000 | 1 | 10% |
Questions
How many prime numbers are there between 7901 and 8,000?
10.
What is the biggest prime number below 8,000?
7993.
What is the first prime number after 7900?
7901.