Prime numbers between 21001 and 22,000
There are 104 prime numbers between 21001 and 22,000: 21001, 21011, 21013, 21017, 21019, 21023, 21031, 21059, 21061, 21067, 21089, 21101, 21107, 21121, 21139, 21143, 21149, 21157, 21163, 21169, 21179, 21187, 21191, 21193, 21211, 21221, 21227, 21247, 21269, 21277, 21283, 21313, 21317, 21319, 21323, 21341, 21347, 21377, 21379, 21383, 21391, 21397, 21401, 21407, 21419, 21433, 21467, 21481, 21487, 21491, 21493, 21499, 21503, 21517, 21521, 21523, 21529, 21557, 21559, 21563, 21569, 21577, 21587, 21589, 21599, 21601, 21611, 21613, 21617, 21647, 21649, 21661, 21673, 21683, 21701, 21713, 21727, 21737, 21739, 21751, 21757, 21767, 21773, 21787, 21799, 21803, 21817, 21821, 21839, 21841, 21851, 21859, 21863, 21871, 21881, 21893, 21911, 21929, 21937, 21943, 21961, 21977, 21991, 21997.
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 ā22000 ā 148.3 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 104 primes between 21001 and 22,000, with a total of 2,234,774.
- 3
The biggest gap between neighbouring primes in this range is 34, after 21433 (the next prime is 21467). There are 15 twin prime pairs (primes 2 apart), the first ones (21011, 21013), (21017, 21019), (21059, 21061), (21191, 21193), (21317, 21319), (21377, 21379), (21491, 21493), (21521, 21523).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 21,001 to 22,000 | 104 | 10.4% |
Questions
How many prime numbers are there between 21001 and 22,000?
104.
What is the biggest prime number below 22,000?
21997.
What is the first prime number after 21000?
21001.