Prime numbers between 32001 and 33,000
There are 106 prime numbers between 32001 and 33,000: 32003, 32009, 32027, 32029, 32051, 32057, 32059, 32063, 32069, 32077, 32083, 32089, 32099, 32117, 32119, 32141, 32143, 32159, 32173, 32183, 32189, 32191, 32203, 32213, 32233, 32237, 32251, 32257, 32261, 32297, 32299, 32303, 32309, 32321, 32323, 32327, 32341, 32353, 32359, 32363, 32369, 32371, 32377, 32381, 32401, 32411, 32413, 32423, 32429, 32441, 32443, 32467, 32479, 32491, 32497, 32503, 32507, 32531, 32533, 32537, 32561, 32563, 32569, 32573, 32579, 32587, 32603, 32609, 32611, 32621, 32633, 32647, 32653, 32687, 32693, 32707, 32713, 32717, 32719, 32749, 32771, 32779, 32783, 32789, 32797, 32801, 32803, 32831, 32833, 32839, 32843, 32869, 32887, 32909, 32911, 32917, 32933, 32939, 32941, 32957, 32969, 32971, 32983, 32987, 32993, 32999.
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 ā33000 ā 181.7 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 106 primes between 32001 and 33,000, with a total of 3,444,212.
- 3
The biggest gap between neighbouring primes in this range is 36, after 32261 (the next prime is 32297). There are 19 twin prime pairs (primes 2 apart), the first ones (32027, 32029), (32057, 32059), (32117, 32119), (32141, 32143), (32189, 32191), (32297, 32299), (32321, 32323), (32369, 32371).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 32,001 to 33,000 | 106 | 10.6% |
Questions
How many prime numbers are there between 32001 and 33,000?
106.
What is the biggest prime number below 33,000?
32999.
What is the first prime number after 32000?
32003.