Prime numbers between 20001 and 21,000
There are 98 prime numbers between 20001 and 21,000: 20011, 20021, 20023, 20029, 20047, 20051, 20063, 20071, 20089, 20101, 20107, 20113, 20117, 20123, 20129, 20143, 20147, 20149, 20161, 20173, 20177, 20183, 20201, 20219, 20231, 20233, 20249, 20261, 20269, 20287, 20297, 20323, 20327, 20333, 20341, 20347, 20353, 20357, 20359, 20369, 20389, 20393, 20399, 20407, 20411, 20431, 20441, 20443, 20477, 20479, 20483, 20507, 20509, 20521, 20533, 20543, 20549, 20551, 20563, 20593, 20599, 20611, 20627, 20639, 20641, 20663, 20681, 20693, 20707, 20717, 20719, 20731, 20743, 20747, 20749, 20753, 20759, 20771, 20773, 20789, 20807, 20809, 20849, 20857, 20873, 20879, 20887, 20897, 20899, 20903, 20921, 20929, 20939, 20947, 20959, 20963, 20981, 20983.
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 ā21000 ā 144.9 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 98 primes between 20001 and 21,000, with a total of 2,007,600.
- 3
The biggest gap between neighbouring primes in this range is 40, after 20809 (the next prime is 20849). There are 15 twin prime pairs (primes 2 apart), the first ones (20021, 20023), (20147, 20149), (20231, 20233), (20357, 20359), (20441, 20443), (20477, 20479), (20507, 20509), (20549, 20551).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 20,001 to 21,000 | 98 | 9.8% |
Questions
How many prime numbers are there between 20001 and 21,000?
98.
What is the biggest prime number below 21,000?
20983.
What is the first prime number after 20000?
20011.