Prime numbers between 81001 and 82,000
There are 92 prime numbers between 81001 and 82,000: 81001, 81013, 81017, 81019, 81023, 81031, 81041, 81043, 81047, 81049, 81071, 81077, 81083, 81097, 81101, 81119, 81131, 81157, 81163, 81173, 81181, 81197, 81199, 81203, 81223, 81233, 81239, 81281, 81283, 81293, 81299, 81307, 81331, 81343, 81349, 81353, 81359, 81371, 81373, 81401, 81409, 81421, 81439, 81457, 81463, 81509, 81517, 81527, 81533, 81547, 81551, 81553, 81559, 81563, 81569, 81611, 81619, 81629, 81637, 81647, 81649, 81667, 81671, 81677, 81689, 81701, 81703, 81707, 81727, 81737, 81749, 81761, 81769, 81773, 81799, 81817, 81839, 81847, 81853, 81869, 81883, 81899, 81901, 81919, 81929, 81931, 81937, 81943, 81953, 81967, 81971, 81973.
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 ā82000 ā 286.4 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 92 primes between 81001 and 82,000, with a total of 7,496,244.
- 3
The biggest gap between neighbouring primes in this range is 46, after 81463 (the next prime is 81509). There are 12 twin prime pairs (primes 2 apart): (81017, 81019), (81041, 81043), (81047, 81049), (81197, 81199), (81281, 81283), (81371, 81373), (81551, 81553), (81647, 81649), (81701, 81703), (81899, 81901), (81929, 81931), (81971, 81973).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 81,001 to 82,000 | 92 | 9.2% |
Questions
How many prime numbers are there between 81001 and 82,000?
92.
What is the biggest prime number below 82,000?
81973.
What is the first prime number after 81000?
81001.