Prime numbers between 6801 and 6,900
There are 12 prime numbers between 6801 and 6,900: 6803, 6823, 6827, 6829, 6833, 6841, 6857, 6863, 6869, 6871, 6883, 6899.
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 ā6900 ā 83.1 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 12 primes between 6801 and 6,900, with a total of 82,198.
- 3
The biggest gap between neighbouring primes in this range is 20, after 6803 (the next prime is 6823). There are 2 twin prime pairs (primes 2 apart): (6827, 6829), (6869, 6871).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 6,801 to 6,810 | 1 | 10% |
| 6,811 to 6,820 | 0 | 0% |
| 6,821 to 6,830 | 3 | 30% |
| 6,831 to 6,840 | 1 | 10% |
| 6,841 to 6,850 | 1 | 10% |
| 6,851 to 6,860 | 1 | 10% |
| 6,861 to 6,870 | 2 | 20% |
| 6,871 to 6,880 | 1 | 10% |
| 6,881 to 6,890 | 1 | 10% |
| 6,891 to 6,900 | 1 | 10% |
Questions
How many prime numbers are there between 6801 and 6,900?
12.
What is the biggest prime number below 6,900?
6899.
What is the first prime number after 6800?
6803.