Prime numbers between 57001 and 58,000
There are 91 prime numbers between 57001 and 58,000: 57037, 57041, 57047, 57059, 57073, 57077, 57089, 57097, 57107, 57119, 57131, 57139, 57143, 57149, 57163, 57173, 57179, 57191, 57193, 57203, 57221, 57223, 57241, 57251, 57259, 57269, 57271, 57283, 57287, 57301, 57329, 57331, 57347, 57349, 57367, 57373, 57383, 57389, 57397, 57413, 57427, 57457, 57467, 57487, 57493, 57503, 57527, 57529, 57557, 57559, 57571, 57587, 57593, 57601, 57637, 57641, 57649, 57653, 57667, 57679, 57689, 57697, 57709, 57713, 57719, 57727, 57731, 57737, 57751, 57773, 57781, 57787, 57791, 57793, 57803, 57809, 57829, 57839, 57847, 57853, 57859, 57881, 57899, 57901, 57917, 57923, 57943, 57947, 57973, 57977, 57991.
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 ā58000 ā 240.8 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 91 primes between 57001 and 58,000, with a total of 5,232,567.
- 3
The biggest gap between neighbouring primes in this range is 36, after 57601 (the next prime is 57637). There are 9 twin prime pairs (primes 2 apart): (57191, 57193), (57221, 57223), (57269, 57271), (57329, 57331), (57347, 57349), (57527, 57529), (57557, 57559), (57791, 57793), (57899, 57901).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 57,001 to 58,000 | 91 | 9.1% |
Questions
How many prime numbers are there between 57001 and 58,000?
91.
What is the biggest prime number below 58,000?
57991.
What is the first prime number after 57000?
57037.