Prime numbers between 89001 and 90,000
There are 94 prime numbers between 89001 and 90,000: 89003, 89009, 89017, 89021, 89041, 89051, 89057, 89069, 89071, 89083, 89087, 89101, 89107, 89113, 89119, 89123, 89137, 89153, 89189, 89203, 89209, 89213, 89227, 89231, 89237, 89261, 89269, 89273, 89293, 89303, 89317, 89329, 89363, 89371, 89381, 89387, 89393, 89399, 89413, 89417, 89431, 89443, 89449, 89459, 89477, 89491, 89501, 89513, 89519, 89521, 89527, 89533, 89561, 89563, 89567, 89591, 89597, 89599, 89603, 89611, 89627, 89633, 89653, 89657, 89659, 89669, 89671, 89681, 89689, 89753, 89759, 89767, 89779, 89783, 89797, 89809, 89819, 89821, 89833, 89839, 89849, 89867, 89891, 89897, 89899, 89909, 89917, 89923, 89939, 89959, 89963, 89977, 89983, 89989.
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 ā90000 ā 300.0 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 94 primes between 89001 and 90,000, with a total of 8,412,256.
- 3
The biggest gap between neighbouring primes in this range is 64, after 89689 (the next prime is 89753). There are 8 twin prime pairs (primes 2 apart): (89069, 89071), (89519, 89521), (89561, 89563), (89597, 89599), (89657, 89659), (89669, 89671), (89819, 89821), (89897, 89899).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 89,001 to 90,000 | 94 | 9.4% |
Questions
How many prime numbers are there between 89001 and 90,000?
94.
What is the biggest prime number below 90,000?
89989.
What is the first prime number after 89000?
89003.