Prime numbers between 74001 and 75,000
There are 92 prime numbers between 74001 and 75,000: 74017, 74021, 74027, 74047, 74051, 74071, 74077, 74093, 74099, 74101, 74131, 74143, 74149, 74159, 74161, 74167, 74177, 74189, 74197, 74201, 74203, 74209, 74219, 74231, 74257, 74279, 74287, 74293, 74297, 74311, 74317, 74323, 74353, 74357, 74363, 74377, 74381, 74383, 74411, 74413, 74419, 74441, 74449, 74453, 74471, 74489, 74507, 74509, 74521, 74527, 74531, 74551, 74561, 74567, 74573, 74587, 74597, 74609, 74611, 74623, 74653, 74687, 74699, 74707, 74713, 74717, 74719, 74729, 74731, 74747, 74759, 74761, 74771, 74779, 74797, 74821, 74827, 74831, 74843, 74857, 74861, 74869, 74873, 74887, 74891, 74897, 74903, 74923, 74929, 74933, 74941, 74959.
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 ā75000 ā 273.9 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 92 primes between 74001 and 75,000, with a total of 6,853,152.
- 3
The biggest gap between neighbouring primes in this range is 34, after 74653 (the next prime is 74687). There are 10 twin prime pairs (primes 2 apart): (74099, 74101), (74159, 74161), (74201, 74203), (74381, 74383), (74411, 74413), (74507, 74509), (74609, 74611), (74717, 74719), (74729, 74731), (74759, 74761).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 74,001 to 75,000 | 92 | 9.2% |
Questions
How many prime numbers are there between 74001 and 75,000?
92.
What is the biggest prime number below 75,000?
74959.
What is the first prime number after 74000?
74017.