Prime numbers between 8101 and 8,200
There are 10 prime numbers between 8101 and 8,200: 8101, 8111, 8117, 8123, 8147, 8161, 8167, 8171, 8179, 8191.
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 ā8200 ā 90.6 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 10 primes between 8101 and 8,200, with a total of 81,468.
- 3
The biggest gap between neighbouring primes in this range is 24, after 8123 (the next prime is 8147). There are no twin primes here.
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 8,101 to 8,110 | 1 | 10% |
| 8,111 to 8,120 | 2 | 20% |
| 8,121 to 8,130 | 1 | 10% |
| 8,131 to 8,140 | 0 | 0% |
| 8,141 to 8,150 | 1 | 10% |
| 8,151 to 8,160 | 0 | 0% |
| 8,161 to 8,170 | 2 | 20% |
| 8,171 to 8,180 | 2 | 20% |
| 8,181 to 8,190 | 0 | 0% |
| 8,191 to 8,200 | 1 | 10% |
Questions
How many prime numbers are there between 8101 and 8,200?
10.
What is the biggest prime number below 8,200?
8191.
What is the first prime number after 8100?
8101.