Prime numbers between 4601 and 4,700
There are 12 prime numbers between 4601 and 4,700: 4603, 4621, 4637, 4639, 4643, 4649, 4651, 4657, 4663, 4673, 4679, 4691.
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 ā4700 ā 68.6 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 12 primes between 4601 and 4,700, with a total of 55,806.
- 3
The biggest gap between neighbouring primes in this range is 18, after 4603 (the next prime is 4621). There are 2 twin prime pairs (primes 2 apart): (4637, 4639), (4649, 4651).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 4,601 to 4,610 | 1 | 10% |
| 4,611 to 4,620 | 0 | 0% |
| 4,621 to 4,630 | 1 | 10% |
| 4,631 to 4,640 | 2 | 20% |
| 4,641 to 4,650 | 2 | 20% |
| 4,651 to 4,660 | 2 | 20% |
| 4,661 to 4,670 | 1 | 10% |
| 4,671 to 4,680 | 2 | 20% |
| 4,681 to 4,690 | 0 | 0% |
| 4,691 to 4,700 | 1 | 10% |
Questions
How many prime numbers are there between 4601 and 4,700?
12.
What is the biggest prime number below 4,700?
4691.
What is the first prime number after 4600?
4603.