Prime numbers between 6301 and 6,400
There are 15 prime numbers between 6301 and 6,400: 6301, 6311, 6317, 6323, 6329, 6337, 6343, 6353, 6359, 6361, 6367, 6373, 6379, 6389, 6397.
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 ā6400 ā 80.0 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 15 primes between 6301 and 6,400, with a total of 95,239.
- 3
The biggest gap between neighbouring primes in this range is 10, after 6301 (the next prime is 6311). There are 1 twin prime pairs (primes 2 apart): (6359, 6361).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 6,301 to 6,310 | 1 | 10% |
| 6,311 to 6,320 | 2 | 20% |
| 6,321 to 6,330 | 2 | 20% |
| 6,331 to 6,340 | 1 | 10% |
| 6,341 to 6,350 | 1 | 10% |
| 6,351 to 6,360 | 2 | 20% |
| 6,361 to 6,370 | 2 | 20% |
| 6,371 to 6,380 | 2 | 20% |
| 6,381 to 6,390 | 1 | 10% |
| 6,391 to 6,400 | 1 | 10% |
Questions
How many prime numbers are there between 6301 and 6,400?
15.
What is the biggest prime number below 6,400?
6397.
What is the first prime number after 6300?
6301.