Prime numbers between 64001 and 65,000
There are 80 prime numbers between 64001 and 65,000: 64007, 64013, 64019, 64033, 64037, 64063, 64067, 64081, 64091, 64109, 64123, 64151, 64153, 64157, 64171, 64187, 64189, 64217, 64223, 64231, 64237, 64271, 64279, 64283, 64301, 64303, 64319, 64327, 64333, 64373, 64381, 64399, 64403, 64433, 64439, 64451, 64453, 64483, 64489, 64499, 64513, 64553, 64567, 64577, 64579, 64591, 64601, 64609, 64613, 64621, 64627, 64633, 64661, 64663, 64667, 64679, 64693, 64709, 64717, 64747, 64763, 64781, 64783, 64793, 64811, 64817, 64849, 64853, 64871, 64877, 64879, 64891, 64901, 64919, 64921, 64927, 64937, 64951, 64969, 64997.
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 ā65000 ā 255.0 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 80 primes between 64001 and 65,000, with a total of 5,159,888.
- 3
The biggest gap between neighbouring primes in this range is 40, after 64333 (the next prime is 64373). There are 9 twin prime pairs (primes 2 apart): (64151, 64153), (64187, 64189), (64301, 64303), (64451, 64453), (64577, 64579), (64661, 64663), (64781, 64783), (64877, 64879), (64919, 64921).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 64,001 to 65,000 | 80 | 8% |
Questions
How many prime numbers are there between 64001 and 65,000?
80.
What is the biggest prime number below 65,000?
64997.
What is the first prime number after 64000?
64007.