Prime numbers between 86001 and 87,000
There are 88 prime numbers between 86001 and 87,000: 86011, 86017, 86027, 86029, 86069, 86077, 86083, 86111, 86113, 86117, 86131, 86137, 86143, 86161, 86171, 86179, 86183, 86197, 86201, 86209, 86239, 86243, 86249, 86257, 86263, 86269, 86287, 86291, 86293, 86297, 86311, 86323, 86341, 86351, 86353, 86357, 86369, 86371, 86381, 86389, 86399, 86413, 86423, 86441, 86453, 86461, 86467, 86477, 86491, 86501, 86509, 86531, 86533, 86539, 86561, 86573, 86579, 86587, 86599, 86627, 86629, 86677, 86689, 86693, 86711, 86719, 86729, 86743, 86753, 86767, 86771, 86783, 86813, 86837, 86843, 86851, 86857, 86861, 86869, 86923, 86927, 86929, 86939, 86951, 86959, 86969, 86981, 86993.
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 ā87000 ā 295.0 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 88 primes between 86001 and 87,000, with a total of 7,609,930.
- 3
The biggest gap between neighbouring primes in this range is 54, after 86869 (the next prime is 86923). There are 8 twin prime pairs (primes 2 apart): (86027, 86029), (86111, 86113), (86291, 86293), (86351, 86353), (86369, 86371), (86531, 86533), (86627, 86629), (86927, 86929).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 86,001 to 87,000 | 88 | 8.8% |
Questions
How many prime numbers are there between 86001 and 87,000?
88.
What is the biggest prime number below 87,000?
86993.
What is the first prime number after 86000?
86011.