Prime numbers between 2001 and 2,100
There are 14 prime numbers between 2001 and 2,100: 2003, 2011, 2017, 2027, 2029, 2039, 2053, 2063, 2069, 2081, 2083, 2087, 2089, 2099.
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 ā2100 ā 45.8 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 14 primes between 2001 and 2,100, with a total of 28,750.
- 3
The biggest gap between neighbouring primes in this range is 14, after 2039 (the next prime is 2053). There are 3 twin prime pairs (primes 2 apart): (2027, 2029), (2081, 2083), (2087, 2089).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 2,001 to 2,010 | 1 | 10% |
| 2,011 to 2,020 | 2 | 20% |
| 2,021 to 2,030 | 2 | 20% |
| 2,031 to 2,040 | 1 | 10% |
| 2,041 to 2,050 | 0 | 0% |
| 2,051 to 2,060 | 1 | 10% |
| 2,061 to 2,070 | 2 | 20% |
| 2,071 to 2,080 | 0 | 0% |
| 2,081 to 2,090 | 4 | 40% |
| 2,091 to 2,100 | 1 | 10% |
Questions
How many prime numbers are there between 2001 and 2,100?
14.
What is the biggest prime number below 2,100?
2099.
What is the first prime number after 2000?
2003.