Prime numbers between 58001 and 59,000
There are 90 prime numbers between 58001 and 59,000: 58013, 58027, 58031, 58043, 58049, 58057, 58061, 58067, 58073, 58099, 58109, 58111, 58129, 58147, 58151, 58153, 58169, 58171, 58189, 58193, 58199, 58207, 58211, 58217, 58229, 58231, 58237, 58243, 58271, 58309, 58313, 58321, 58337, 58363, 58367, 58369, 58379, 58391, 58393, 58403, 58411, 58417, 58427, 58439, 58441, 58451, 58453, 58477, 58481, 58511, 58537, 58543, 58549, 58567, 58573, 58579, 58601, 58603, 58613, 58631, 58657, 58661, 58679, 58687, 58693, 58699, 58711, 58727, 58733, 58741, 58757, 58763, 58771, 58787, 58789, 58831, 58889, 58897, 58901, 58907, 58909, 58913, 58921, 58937, 58943, 58963, 58967, 58979, 58991, 58997.
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 ā59000 ā 242.9 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 90 primes between 58001 and 59,000, with a total of 5,263,136.
- 3
The biggest gap between neighbouring primes in this range is 58, after 58831 (the next prime is 58889). There are 11 twin prime pairs (primes 2 apart): (58109, 58111), (58151, 58153), (58169, 58171), (58229, 58231), (58367, 58369), (58391, 58393), (58439, 58441), (58451, 58453), (58601, 58603), (58787, 58789), (58907, 58909).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 58,001 to 59,000 | 90 | 9% |
Questions
How many prime numbers are there between 58001 and 59,000?
90.
What is the biggest prime number below 59,000?
58997.
What is the first prime number after 58000?
58013.