Prime numbers between 12001 and 13,000
There are 109 prime numbers between 12001 and 13,000: 12007, 12011, 12037, 12041, 12043, 12049, 12071, 12073, 12097, 12101, 12107, 12109, 12113, 12119, 12143, 12149, 12157, 12161, 12163, 12197, 12203, 12211, 12227, 12239, 12241, 12251, 12253, 12263, 12269, 12277, 12281, 12289, 12301, 12323, 12329, 12343, 12347, 12373, 12377, 12379, 12391, 12401, 12409, 12413, 12421, 12433, 12437, 12451, 12457, 12473, 12479, 12487, 12491, 12497, 12503, 12511, 12517, 12527, 12539, 12541, 12547, 12553, 12569, 12577, 12583, 12589, 12601, 12611, 12613, 12619, 12637, 12641, 12647, 12653, 12659, 12671, 12689, 12697, 12703, 12713, 12721, 12739, 12743, 12757, 12763, 12781, 12791, 12799, 12809, 12821, 12823, 12829, 12841, 12853, 12889, 12893, 12899, 12907, 12911, 12917, 12919, 12923, 12941, 12953, 12959, 12967, 12973, 12979, 12983.
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 ā13000 ā 114.0 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 109 primes between 12001 and 13,000, with a total of 1,362,757.
- 3
The biggest gap between neighbouring primes in this range is 36, after 12853 (the next prime is 12889). There are 11 twin prime pairs (primes 2 apart): (12041, 12043), (12071, 12073), (12107, 12109), (12161, 12163), (12239, 12241), (12251, 12253), (12377, 12379), (12539, 12541), (12611, 12613), (12821, 12823), (12917, 12919).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 12,001 to 13,000 | 109 | 10.9% |
Questions
How many prime numbers are there between 12001 and 13,000?
109.
What is the biggest prime number below 13,000?
12983.
What is the first prime number after 12000?
12007.