Prime numbers between 11001 and 12,000
There are 103 prime numbers between 11001 and 12,000: 11003, 11027, 11047, 11057, 11059, 11069, 11071, 11083, 11087, 11093, 11113, 11117, 11119, 11131, 11149, 11159, 11161, 11171, 11173, 11177, 11197, 11213, 11239, 11243, 11251, 11257, 11261, 11273, 11279, 11287, 11299, 11311, 11317, 11321, 11329, 11351, 11353, 11369, 11383, 11393, 11399, 11411, 11423, 11437, 11443, 11447, 11467, 11471, 11483, 11489, 11491, 11497, 11503, 11519, 11527, 11549, 11551, 11579, 11587, 11593, 11597, 11617, 11621, 11633, 11657, 11677, 11681, 11689, 11699, 11701, 11717, 11719, 11731, 11743, 11777, 11779, 11783, 11789, 11801, 11807, 11813, 11821, 11827, 11831, 11833, 11839, 11863, 11867, 11887, 11897, 11903, 11909, 11923, 11927, 11933, 11939, 11941, 11953, 11959, 11969, 11971, 11981, 11987.
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 ā12000 ā 109.5 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 103 primes between 11001 and 12,000, with a total of 1,185,849.
- 3
The biggest gap between neighbouring primes in this range is 34, after 11743 (the next prime is 11777). There are 14 twin prime pairs (primes 2 apart), the first ones (11057, 11059), (11069, 11071), (11117, 11119), (11159, 11161), (11171, 11173), (11351, 11353), (11489, 11491), (11549, 11551).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 11,001 to 12,000 | 103 | 10.3% |
Questions
How many prime numbers are there between 11001 and 12,000?
103.
What is the biggest prime number below 12,000?
11987.
What is the first prime number after 11000?
11003.