Prime numbers between 6001 and 6,100
There are 12 prime numbers between 6001 and 6,100: 6007, 6011, 6029, 6037, 6043, 6047, 6053, 6067, 6073, 6079, 6089, 6091.
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 ā6100 ā 78.1 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 12 primes between 6001 and 6,100, with a total of 72,626.
- 3
The biggest gap between neighbouring primes in this range is 18, after 6011 (the next prime is 6029). There are 1 twin prime pairs (primes 2 apart): (6089, 6091).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 6,001 to 6,010 | 1 | 10% |
| 6,011 to 6,020 | 1 | 10% |
| 6,021 to 6,030 | 1 | 10% |
| 6,031 to 6,040 | 1 | 10% |
| 6,041 to 6,050 | 2 | 20% |
| 6,051 to 6,060 | 1 | 10% |
| 6,061 to 6,070 | 1 | 10% |
| 6,071 to 6,080 | 2 | 20% |
| 6,081 to 6,090 | 1 | 10% |
| 6,091 to 6,100 | 1 | 10% |
Questions
How many prime numbers are there between 6001 and 6,100?
12.
What is the biggest prime number below 6,100?
6091.
What is the first prime number after 6000?
6007.