Prime numbers between 75001 and 76,000
There are 91 prime numbers between 75001 and 76,000: 75011, 75013, 75017, 75029, 75037, 75041, 75079, 75083, 75109, 75133, 75149, 75161, 75167, 75169, 75181, 75193, 75209, 75211, 75217, 75223, 75227, 75239, 75253, 75269, 75277, 75289, 75307, 75323, 75329, 75337, 75347, 75353, 75367, 75377, 75389, 75391, 75401, 75403, 75407, 75431, 75437, 75479, 75503, 75511, 75521, 75527, 75533, 75539, 75541, 75553, 75557, 75571, 75577, 75583, 75611, 75617, 75619, 75629, 75641, 75653, 75659, 75679, 75683, 75689, 75703, 75707, 75709, 75721, 75731, 75743, 75767, 75773, 75781, 75787, 75793, 75797, 75821, 75833, 75853, 75869, 75883, 75913, 75931, 75937, 75941, 75967, 75979, 75983, 75989, 75991, 75997.
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 ā76000 ā 275.7 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 91 primes between 75001 and 76,000, with a total of 6,870,959.
- 3
The biggest gap between neighbouring primes in this range is 42, after 75437 (the next prime is 75479). There are 9 twin prime pairs (primes 2 apart): (75011, 75013), (75167, 75169), (75209, 75211), (75389, 75391), (75401, 75403), (75539, 75541), (75617, 75619), (75707, 75709), (75989, 75991).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 75,001 to 76,000 | 91 | 9.1% |
Questions
How many prime numbers are there between 75001 and 76,000?
91.
What is the biggest prime number below 76,000?
75997.
What is the first prime number after 75000?
75011.