Prime numbers between 19001 and 20,000
There are 104 prime numbers between 19001 and 20,000: 19001, 19009, 19013, 19031, 19037, 19051, 19069, 19073, 19079, 19081, 19087, 19121, 19139, 19141, 19157, 19163, 19181, 19183, 19207, 19211, 19213, 19219, 19231, 19237, 19249, 19259, 19267, 19273, 19289, 19301, 19309, 19319, 19333, 19373, 19379, 19381, 19387, 19391, 19403, 19417, 19421, 19423, 19427, 19429, 19433, 19441, 19447, 19457, 19463, 19469, 19471, 19477, 19483, 19489, 19501, 19507, 19531, 19541, 19543, 19553, 19559, 19571, 19577, 19583, 19597, 19603, 19609, 19661, 19681, 19687, 19697, 19699, 19709, 19717, 19727, 19739, 19751, 19753, 19759, 19763, 19777, 19793, 19801, 19813, 19819, 19841, 19843, 19853, 19861, 19867, 19889, 19891, 19913, 19919, 19927, 19937, 19949, 19961, 19963, 19973, 19979, 19991, 19993, 19997.
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 ā20000 ā 141.4 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 104 primes between 19001 and 20,000, with a total of 2,028,762.
- 3
The biggest gap between neighbouring primes in this range is 52, after 19609 (the next prime is 19661). There are 15 twin prime pairs (primes 2 apart), the first ones (19079, 19081), (19139, 19141), (19181, 19183), (19211, 19213), (19379, 19381), (19421, 19423), (19427, 19429), (19469, 19471).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 19,001 to 20,000 | 104 | 10.4% |
Questions
How many prime numbers are there between 19001 and 20,000?
104.
What is the biggest prime number below 20,000?
19997.
What is the first prime number after 19000?
19001.