Prime numbers between 83001 and 84,000
There are 84 prime numbers between 83001 and 84,000: 83003, 83009, 83023, 83047, 83059, 83063, 83071, 83077, 83089, 83093, 83101, 83117, 83137, 83177, 83203, 83207, 83219, 83221, 83227, 83231, 83233, 83243, 83257, 83267, 83269, 83273, 83299, 83311, 83339, 83341, 83357, 83383, 83389, 83399, 83401, 83407, 83417, 83423, 83431, 83437, 83443, 83449, 83459, 83471, 83477, 83497, 83537, 83557, 83561, 83563, 83579, 83591, 83597, 83609, 83617, 83621, 83639, 83641, 83653, 83663, 83689, 83701, 83717, 83719, 83737, 83761, 83773, 83777, 83791, 83813, 83833, 83843, 83857, 83869, 83873, 83891, 83903, 83911, 83921, 83933, 83939, 83969, 83983, 83987.
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 ā84000 ā 289.8 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 84 primes between 83001 and 84,000, with a total of 7,012,664.
- 3
The biggest gap between neighbouring primes in this range is 40, after 83137 (the next prime is 83177). There are 8 twin prime pairs (primes 2 apart): (83219, 83221), (83231, 83233), (83267, 83269), (83339, 83341), (83399, 83401), (83561, 83563), (83639, 83641), (83717, 83719).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 83,001 to 84,000 | 84 | 8.4% |
Questions
How many prime numbers are there between 83001 and 84,000?
84.
What is the biggest prime number below 84,000?
83987.
What is the first prime number after 83000?
83003.