Prime numbers between 6601 and 6,700
There are 10 prime numbers between 6601 and 6,700: 6607, 6619, 6637, 6653, 6659, 6661, 6673, 6679, 6689, 6691.
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 ā6700 ā 81.9 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 10 primes between 6601 and 6,700, with a total of 66,568.
- 3
The biggest gap between neighbouring primes in this range is 18, after 6619 (the next prime is 6637). There are 2 twin prime pairs (primes 2 apart): (6659, 6661), (6689, 6691).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 6,601 to 6,610 | 1 | 10% |
| 6,611 to 6,620 | 1 | 10% |
| 6,621 to 6,630 | 0 | 0% |
| 6,631 to 6,640 | 1 | 10% |
| 6,641 to 6,650 | 0 | 0% |
| 6,651 to 6,660 | 2 | 20% |
| 6,661 to 6,670 | 1 | 10% |
| 6,671 to 6,680 | 2 | 20% |
| 6,681 to 6,690 | 1 | 10% |
| 6,691 to 6,700 | 1 | 10% |
Questions
How many prime numbers are there between 6601 and 6,700?
10.
What is the biggest prime number below 6,700?
6691.
What is the first prime number after 6600?
6607.