Prime numbers between 9601 and 9,700
There are 13 prime numbers between 9601 and 9,700: 9601, 9613, 9619, 9623, 9629, 9631, 9643, 9649, 9661, 9677, 9679, 9689, 9697.
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 ā9700 ā 98.5 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 13 primes between 9601 and 9,700, with a total of 125,411.
- 3
The biggest gap between neighbouring primes in this range is 16, after 9661 (the next prime is 9677). There are 2 twin prime pairs (primes 2 apart): (9629, 9631), (9677, 9679).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 9,601 to 9,610 | 1 | 10% |
| 9,611 to 9,620 | 2 | 20% |
| 9,621 to 9,630 | 2 | 20% |
| 9,631 to 9,640 | 1 | 10% |
| 9,641 to 9,650 | 2 | 20% |
| 9,651 to 9,660 | 0 | 0% |
| 9,661 to 9,670 | 1 | 10% |
| 9,671 to 9,680 | 2 | 20% |
| 9,681 to 9,690 | 1 | 10% |
| 9,691 to 9,700 | 1 | 10% |
Questions
How many prime numbers are there between 9601 and 9,700?
13.
What is the biggest prime number below 9,700?
9697.
What is the first prime number after 9600?
9601.