Prime numbers between 43001 and 44,000
There are 85 prime numbers between 43001 and 44,000: 43003, 43013, 43019, 43037, 43049, 43051, 43063, 43067, 43093, 43103, 43117, 43133, 43151, 43159, 43177, 43189, 43201, 43207, 43223, 43237, 43261, 43271, 43283, 43291, 43313, 43319, 43321, 43331, 43391, 43397, 43399, 43403, 43411, 43427, 43441, 43451, 43457, 43481, 43487, 43499, 43517, 43541, 43543, 43573, 43577, 43579, 43591, 43597, 43607, 43609, 43613, 43627, 43633, 43649, 43651, 43661, 43669, 43691, 43711, 43717, 43721, 43753, 43759, 43777, 43781, 43783, 43787, 43789, 43793, 43801, 43853, 43867, 43889, 43891, 43913, 43933, 43943, 43951, 43961, 43963, 43969, 43973, 43987, 43991, 43997.
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 ā44000 ā 209.8 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 85 primes between 43001 and 44,000, with a total of 3,699,107.
- 3
The biggest gap between neighbouring primes in this range is 60, after 43331 (the next prime is 43391). There are 11 twin prime pairs (primes 2 apart): (43049, 43051), (43319, 43321), (43397, 43399), (43541, 43543), (43577, 43579), (43607, 43609), (43649, 43651), (43781, 43783), (43787, 43789), (43889, 43891), (43961, 43963).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 43,001 to 44,000 | 85 | 8.5% |
Questions
How many prime numbers are there between 43001 and 44,000?
85.
What is the biggest prime number below 44,000?
43997.
What is the first prime number after 43000?
43003.