Prime numbers between 44001 and 45,000
There are 96 prime numbers between 44001 and 45,000: 44017, 44021, 44027, 44029, 44041, 44053, 44059, 44071, 44087, 44089, 44101, 44111, 44119, 44123, 44129, 44131, 44159, 44171, 44179, 44189, 44201, 44203, 44207, 44221, 44249, 44257, 44263, 44267, 44269, 44273, 44279, 44281, 44293, 44351, 44357, 44371, 44381, 44383, 44389, 44417, 44449, 44453, 44483, 44491, 44497, 44501, 44507, 44519, 44531, 44533, 44537, 44543, 44549, 44563, 44579, 44587, 44617, 44621, 44623, 44633, 44641, 44647, 44651, 44657, 44683, 44687, 44699, 44701, 44711, 44729, 44741, 44753, 44771, 44773, 44777, 44789, 44797, 44809, 44819, 44839, 44843, 44851, 44867, 44879, 44887, 44893, 44909, 44917, 44927, 44939, 44953, 44959, 44963, 44971, 44983, 44987.
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 ā45000 ā 212.1 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 96 primes between 44001 and 45,000, with a total of 4,272,036.
- 3
The biggest gap between neighbouring primes in this range is 58, after 44293 (the next prime is 44351). There are 11 twin prime pairs (primes 2 apart): (44027, 44029), (44087, 44089), (44129, 44131), (44201, 44203), (44267, 44269), (44279, 44281), (44381, 44383), (44531, 44533), (44621, 44623), (44699, 44701), (44771, 44773).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 44,001 to 45,000 | 96 | 9.6% |
Questions
How many prime numbers are there between 44001 and 45,000?
96.
What is the biggest prime number below 45,000?
44987.
What is the first prime number after 44000?
44017.