Prime numbers between 7601 and 7,700
There are 12 prime numbers between 7601 and 7,700: 7603, 7607, 7621, 7639, 7643, 7649, 7669, 7673, 7681, 7687, 7691, 7699.
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 ā7700 ā 87.7 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 12 primes between 7601 and 7,700, with a total of 91,862.
- 3
The biggest gap between neighbouring primes in this range is 20, after 7649 (the next prime is 7669). There are no twin primes here.
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 7,601 to 7,610 | 2 | 20% |
| 7,611 to 7,620 | 0 | 0% |
| 7,621 to 7,630 | 1 | 10% |
| 7,631 to 7,640 | 1 | 10% |
| 7,641 to 7,650 | 2 | 20% |
| 7,651 to 7,660 | 0 | 0% |
| 7,661 to 7,670 | 1 | 10% |
| 7,671 to 7,680 | 1 | 10% |
| 7,681 to 7,690 | 2 | 20% |
| 7,691 to 7,700 | 2 | 20% |
Questions
How many prime numbers are there between 7601 and 7,700?
12.
What is the biggest prime number below 7,700?
7699.
What is the first prime number after 7600?
7603.