Prime numbers between 14001 and 15,000
There are 102 prime numbers between 14001 and 15,000: 14009, 14011, 14029, 14033, 14051, 14057, 14071, 14081, 14083, 14087, 14107, 14143, 14149, 14153, 14159, 14173, 14177, 14197, 14207, 14221, 14243, 14249, 14251, 14281, 14293, 14303, 14321, 14323, 14327, 14341, 14347, 14369, 14387, 14389, 14401, 14407, 14411, 14419, 14423, 14431, 14437, 14447, 14449, 14461, 14479, 14489, 14503, 14519, 14533, 14537, 14543, 14549, 14551, 14557, 14561, 14563, 14591, 14593, 14621, 14627, 14629, 14633, 14639, 14653, 14657, 14669, 14683, 14699, 14713, 14717, 14723, 14731, 14737, 14741, 14747, 14753, 14759, 14767, 14771, 14779, 14783, 14797, 14813, 14821, 14827, 14831, 14843, 14851, 14867, 14869, 14879, 14887, 14891, 14897, 14923, 14929, 14939, 14947, 14951, 14957, 14969, 14983.
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 ā15000 ā 122.5 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 102 primes between 14001 and 15,000, with a total of 1,481,378.
- 3
The biggest gap between neighbouring primes in this range is 36, after 14107 (the next prime is 14143). There are 11 twin prime pairs (primes 2 apart): (14009, 14011), (14081, 14083), (14249, 14251), (14321, 14323), (14387, 14389), (14447, 14449), (14549, 14551), (14561, 14563), (14591, 14593), (14627, 14629), (14867, 14869).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 14,001 to 15,000 | 102 | 10.2% |
Questions
How many prime numbers are there between 14001 and 15,000?
102.
What is the biggest prime number below 15,000?
14983.
What is the first prime number after 14000?
14009.