Prime numbers between 8001 and 8,100
There are 11 prime numbers between 8001 and 8,100: 8009, 8011, 8017, 8039, 8053, 8059, 8069, 8081, 8087, 8089, 8093.
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 ā8100 ā 90.0 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 11 primes between 8001 and 8,100, with a total of 88,607.
- 3
The biggest gap between neighbouring primes in this range is 22, after 8017 (the next prime is 8039). There are 2 twin prime pairs (primes 2 apart): (8009, 8011), (8087, 8089).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 8,001 to 8,010 | 1 | 10% |
| 8,011 to 8,020 | 2 | 20% |
| 8,021 to 8,030 | 0 | 0% |
| 8,031 to 8,040 | 1 | 10% |
| 8,041 to 8,050 | 0 | 0% |
| 8,051 to 8,060 | 2 | 20% |
| 8,061 to 8,070 | 1 | 10% |
| 8,071 to 8,080 | 0 | 0% |
| 8,081 to 8,090 | 3 | 30% |
| 8,091 to 8,100 | 1 | 10% |
Questions
How many prime numbers are there between 8001 and 8,100?
11.
What is the biggest prime number below 8,100?
8093.
What is the first prime number after 8000?
8009.