Prime numbers between 6901 and 7,000
There are 13 prime numbers between 6901 and 7,000: 6907, 6911, 6917, 6947, 6949, 6959, 6961, 6967, 6971, 6977, 6983, 6991, 6997.
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 ā7000 ā 83.7 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 13 primes between 6901 and 7,000, with a total of 90,437.
- 3
The biggest gap between neighbouring primes in this range is 30, after 6917 (the next prime is 6947). There are 2 twin prime pairs (primes 2 apart): (6947, 6949), (6959, 6961).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 6,901 to 6,910 | 1 | 10% |
| 6,911 to 6,920 | 2 | 20% |
| 6,921 to 6,930 | 0 | 0% |
| 6,931 to 6,940 | 0 | 0% |
| 6,941 to 6,950 | 2 | 20% |
| 6,951 to 6,960 | 1 | 10% |
| 6,961 to 6,970 | 2 | 20% |
| 6,971 to 6,980 | 2 | 20% |
| 6,981 to 6,990 | 1 | 10% |
| 6,991 to 7,000 | 2 | 20% |
Questions
How many prime numbers are there between 6901 and 7,000?
13.
What is the biggest prime number below 7,000?
6997.
What is the first prime number after 6900?
6907.