Prime numbers between 17001 and 18,000
There are 104 prime numbers between 17001 and 18,000: 17011, 17021, 17027, 17029, 17033, 17041, 17047, 17053, 17077, 17093, 17099, 17107, 17117, 17123, 17137, 17159, 17167, 17183, 17189, 17191, 17203, 17207, 17209, 17231, 17239, 17257, 17291, 17293, 17299, 17317, 17321, 17327, 17333, 17341, 17351, 17359, 17377, 17383, 17387, 17389, 17393, 17401, 17417, 17419, 17431, 17443, 17449, 17467, 17471, 17477, 17483, 17489, 17491, 17497, 17509, 17519, 17539, 17551, 17569, 17573, 17579, 17581, 17597, 17599, 17609, 17623, 17627, 17657, 17659, 17669, 17681, 17683, 17707, 17713, 17729, 17737, 17747, 17749, 17761, 17783, 17789, 17791, 17807, 17827, 17837, 17839, 17851, 17863, 17881, 17891, 17903, 17909, 17911, 17921, 17923, 17929, 17939, 17957, 17959, 17971, 17977, 17981, 17987, 17989.
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 ā18000 ā 134.2 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 104 primes between 17001 and 18,000, with a total of 1,820,728.
- 3
The biggest gap between neighbouring primes in this range is 34, after 17257 (the next prime is 17291). There are 18 twin prime pairs (primes 2 apart), the first ones (17027, 17029), (17189, 17191), (17207, 17209), (17291, 17293), (17387, 17389), (17417, 17419), (17489, 17491), (17579, 17581).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 17,001 to 18,000 | 104 | 10.4% |
Questions
How many prime numbers are there between 17001 and 18,000?
104.
What is the biggest prime number below 18,000?
17989.
What is the first prime number after 17000?
17011.