Prime numbers between 2101 and 2,200
There are 10 prime numbers between 2101 and 2,200: 2111, 2113, 2129, 2131, 2137, 2141, 2143, 2153, 2161, 2179.
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 ā2200 ā 46.9 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 10 primes between 2101 and 2,200, with a total of 21,398.
- 3
The biggest gap between neighbouring primes in this range is 18, after 2161 (the next prime is 2179). There are 3 twin prime pairs (primes 2 apart): (2111, 2113), (2129, 2131), (2141, 2143).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 2,101 to 2,110 | 0 | 0% |
| 2,111 to 2,120 | 2 | 20% |
| 2,121 to 2,130 | 1 | 10% |
| 2,131 to 2,140 | 2 | 20% |
| 2,141 to 2,150 | 2 | 20% |
| 2,151 to 2,160 | 1 | 10% |
| 2,161 to 2,170 | 1 | 10% |
| 2,171 to 2,180 | 1 | 10% |
| 2,181 to 2,190 | 0 | 0% |
| 2,191 to 2,200 | 0 | 0% |
Questions
How many prime numbers are there between 2101 and 2,200?
10.
What is the biggest prime number below 2,200?
2179.
What is the first prime number after 2100?
2111.