Prime numbers between 6701 and 6,800
There are 12 prime numbers between 6701 and 6,800: 6701, 6703, 6709, 6719, 6733, 6737, 6761, 6763, 6779, 6781, 6791, 6793.
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 ā6800 ā 82.5 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 12 primes between 6701 and 6,800, with a total of 80,970.
- 3
The biggest gap between neighbouring primes in this range is 24, after 6737 (the next prime is 6761). There are 4 twin prime pairs (primes 2 apart): (6701, 6703), (6761, 6763), (6779, 6781), (6791, 6793).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 6,701 to 6,710 | 3 | 30% |
| 6,711 to 6,720 | 1 | 10% |
| 6,721 to 6,730 | 0 | 0% |
| 6,731 to 6,740 | 2 | 20% |
| 6,741 to 6,750 | 0 | 0% |
| 6,751 to 6,760 | 0 | 0% |
| 6,761 to 6,770 | 2 | 20% |
| 6,771 to 6,780 | 1 | 10% |
| 6,781 to 6,790 | 1 | 10% |
| 6,791 to 6,800 | 2 | 20% |
Questions
How many prime numbers are there between 6701 and 6,800?
12.
What is the biggest prime number below 6,800?
6793.
What is the first prime number after 6700?
6701.