Prime numbers between 56001 and 57,000
There are 99 prime numbers between 56001 and 57,000: 56003, 56009, 56039, 56041, 56053, 56081, 56087, 56093, 56099, 56101, 56113, 56123, 56131, 56149, 56167, 56171, 56179, 56197, 56207, 56209, 56237, 56239, 56249, 56263, 56267, 56269, 56299, 56311, 56333, 56359, 56369, 56377, 56383, 56393, 56401, 56417, 56431, 56437, 56443, 56453, 56467, 56473, 56477, 56479, 56489, 56501, 56503, 56509, 56519, 56527, 56531, 56533, 56543, 56569, 56591, 56597, 56599, 56611, 56629, 56633, 56659, 56663, 56671, 56681, 56687, 56701, 56711, 56713, 56731, 56737, 56747, 56767, 56773, 56779, 56783, 56807, 56809, 56813, 56821, 56827, 56843, 56857, 56873, 56891, 56893, 56897, 56909, 56911, 56921, 56923, 56929, 56941, 56951, 56957, 56963, 56983, 56989, 56993, 56999.
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 ā57000 ā 238.7 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 99 primes between 56001 and 57,000, with a total of 5,596,465.
- 3
The biggest gap between neighbouring primes in this range is 30, after 56009 (the next prime is 56039). There are 14 twin prime pairs (primes 2 apart), the first ones (56039, 56041), (56099, 56101), (56207, 56209), (56237, 56239), (56267, 56269), (56477, 56479), (56501, 56503), (56531, 56533).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 56,001 to 57,000 | 99 | 9.9% |
Questions
How many prime numbers are there between 56001 and 57,000?
99.
What is the biggest prime number below 57,000?
56999.
What is the first prime number after 56000?
56003.