Prime numbers between 87001 and 88,000
There are 93 prime numbers between 87001 and 88,000: 87011, 87013, 87037, 87041, 87049, 87071, 87083, 87103, 87107, 87119, 87121, 87133, 87149, 87151, 87179, 87181, 87187, 87211, 87221, 87223, 87251, 87253, 87257, 87277, 87281, 87293, 87299, 87313, 87317, 87323, 87337, 87359, 87383, 87403, 87407, 87421, 87427, 87433, 87443, 87473, 87481, 87491, 87509, 87511, 87517, 87523, 87539, 87541, 87547, 87553, 87557, 87559, 87583, 87587, 87589, 87613, 87623, 87629, 87631, 87641, 87643, 87649, 87671, 87679, 87683, 87691, 87697, 87701, 87719, 87721, 87739, 87743, 87751, 87767, 87793, 87797, 87803, 87811, 87833, 87853, 87869, 87877, 87881, 87887, 87911, 87917, 87931, 87943, 87959, 87961, 87973, 87977, 87991.
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 ā88000 ā 296.6 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 93 primes between 87001 and 88,000, with a total of 8,138,385.
- 3
The biggest gap between neighbouring primes in this range is 30, after 87443 (the next prime is 87473). There are 14 twin prime pairs (primes 2 apart), the first ones (87011, 87013), (87119, 87121), (87149, 87151), (87179, 87181), (87221, 87223), (87251, 87253), (87509, 87511), (87539, 87541).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 87,001 to 88,000 | 93 | 9.3% |
Questions
How many prime numbers are there between 87001 and 88,000?
93.
What is the biggest prime number below 88,000?
87991.
What is the first prime number after 87000?
87011.