Prime numbers between 22001 and 23,000
There are 100 prime numbers between 22001 and 23,000: 22003, 22013, 22027, 22031, 22037, 22039, 22051, 22063, 22067, 22073, 22079, 22091, 22093, 22109, 22111, 22123, 22129, 22133, 22147, 22153, 22157, 22159, 22171, 22189, 22193, 22229, 22247, 22259, 22271, 22273, 22277, 22279, 22283, 22291, 22303, 22307, 22343, 22349, 22367, 22369, 22381, 22391, 22397, 22409, 22433, 22441, 22447, 22453, 22469, 22481, 22483, 22501, 22511, 22531, 22541, 22543, 22549, 22567, 22571, 22573, 22613, 22619, 22621, 22637, 22639, 22643, 22651, 22669, 22679, 22691, 22697, 22699, 22709, 22717, 22721, 22727, 22739, 22741, 22751, 22769, 22777, 22783, 22787, 22807, 22811, 22817, 22853, 22859, 22861, 22871, 22877, 22901, 22907, 22921, 22937, 22943, 22961, 22963, 22973, 22993.
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 ā23000 ā 151.7 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 100 primes between 22001 and 23,000, with a total of 2,247,894.
- 3
The biggest gap between neighbouring primes in this range is 40, after 22573 (the next prime is 22613). There are 16 twin prime pairs (primes 2 apart), the first ones (22037, 22039), (22091, 22093), (22109, 22111), (22157, 22159), (22271, 22273), (22277, 22279), (22367, 22369), (22481, 22483).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 22,001 to 23,000 | 100 | 10% |
Questions
How many prime numbers are there between 22001 and 23,000?
100.
What is the biggest prime number below 23,000?
22993.
What is the first prime number after 22000?
22003.