Prime numbers between 84001 and 85,000
There are 87 prime numbers between 84001 and 85,000: 84011, 84017, 84047, 84053, 84059, 84061, 84067, 84089, 84121, 84127, 84131, 84137, 84143, 84163, 84179, 84181, 84191, 84199, 84211, 84221, 84223, 84229, 84239, 84247, 84263, 84299, 84307, 84313, 84317, 84319, 84347, 84349, 84377, 84389, 84391, 84401, 84407, 84421, 84431, 84437, 84443, 84449, 84457, 84463, 84467, 84481, 84499, 84503, 84509, 84521, 84523, 84533, 84551, 84559, 84589, 84629, 84631, 84649, 84653, 84659, 84673, 84691, 84697, 84701, 84713, 84719, 84731, 84737, 84751, 84761, 84787, 84793, 84809, 84811, 84827, 84857, 84859, 84869, 84871, 84913, 84919, 84947, 84961, 84967, 84977, 84979, 84991.
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 ā85000 ā 291.5 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 87 primes between 84001 and 85,000, with a total of 7,350,193.
- 3
The biggest gap between neighbouring primes in this range is 42, after 84871 (the next prime is 84913). There are 12 twin prime pairs (primes 2 apart): (84059, 84061), (84179, 84181), (84221, 84223), (84317, 84319), (84347, 84349), (84389, 84391), (84521, 84523), (84629, 84631), (84809, 84811), (84857, 84859), (84869, 84871), (84977, 84979).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 84,001 to 85,000 | 87 | 8.7% |
Questions
How many prime numbers are there between 84001 and 85,000?
87.
What is the biggest prime number below 85,000?
84991.
What is the first prime number after 84000?
84011.