Prime numbers between 88001 and 89,000
There are 76 prime numbers between 88001 and 89,000: 88001, 88003, 88007, 88019, 88037, 88069, 88079, 88093, 88117, 88129, 88169, 88177, 88211, 88223, 88237, 88241, 88259, 88261, 88289, 88301, 88321, 88327, 88337, 88339, 88379, 88397, 88411, 88423, 88427, 88463, 88469, 88471, 88493, 88499, 88513, 88523, 88547, 88589, 88591, 88607, 88609, 88643, 88651, 88657, 88661, 88663, 88667, 88681, 88721, 88729, 88741, 88747, 88771, 88789, 88793, 88799, 88801, 88807, 88811, 88813, 88817, 88819, 88843, 88853, 88861, 88867, 88873, 88883, 88897, 88903, 88919, 88937, 88951, 88969, 88993, 88997.
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 ā89000 ā 298.3 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 76 primes between 88001 and 89,000, with a total of 6,728,984.
- 3
The biggest gap between neighbouring primes in this range is 42, after 88547 (the next prime is 88589). There are 10 twin prime pairs (primes 2 apart): (88001, 88003), (88259, 88261), (88337, 88339), (88469, 88471), (88589, 88591), (88607, 88609), (88661, 88663), (88799, 88801), (88811, 88813), (88817, 88819).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 88,001 to 89,000 | 76 | 7.6% |
Questions
How many prime numbers are there between 88001 and 89,000?
76.
What is the biggest prime number below 89,000?
88997.
What is the first prime number after 88000?
88001.