Prime numbers between 82001 and 83,000
There are 89 prime numbers between 82001 and 83,000: 82003, 82007, 82009, 82013, 82021, 82031, 82037, 82039, 82051, 82067, 82073, 82129, 82139, 82141, 82153, 82163, 82171, 82183, 82189, 82193, 82207, 82217, 82219, 82223, 82231, 82237, 82241, 82261, 82267, 82279, 82301, 82307, 82339, 82349, 82351, 82361, 82373, 82387, 82393, 82421, 82457, 82463, 82469, 82471, 82483, 82487, 82493, 82499, 82507, 82529, 82531, 82549, 82559, 82561, 82567, 82571, 82591, 82601, 82609, 82613, 82619, 82633, 82651, 82657, 82699, 82721, 82723, 82727, 82729, 82757, 82759, 82763, 82781, 82787, 82793, 82799, 82811, 82813, 82837, 82847, 82883, 82889, 82891, 82903, 82913, 82939, 82963, 82981, 82997.
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 ā83000 ā 288.1 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 89 primes between 82001 and 83,000, with a total of 7,339,651.
- 3
The biggest gap between neighbouring primes in this range is 56, after 82073 (the next prime is 82129). There are 13 twin prime pairs (primes 2 apart), the first ones (82007, 82009), (82037, 82039), (82139, 82141), (82217, 82219), (82349, 82351), (82469, 82471), (82529, 82531), (82559, 82561).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 82,001 to 83,000 | 89 | 8.9% |
Questions
How many prime numbers are there between 82001 and 83,000?
89.
What is the biggest prime number below 83,000?
82997.
What is the first prime number after 82000?
82003.