Prime numbers between 13001 and 14,000
There are 105 prime numbers between 13001 and 14,000: 13001, 13003, 13007, 13009, 13033, 13037, 13043, 13049, 13063, 13093, 13099, 13103, 13109, 13121, 13127, 13147, 13151, 13159, 13163, 13171, 13177, 13183, 13187, 13217, 13219, 13229, 13241, 13249, 13259, 13267, 13291, 13297, 13309, 13313, 13327, 13331, 13337, 13339, 13367, 13381, 13397, 13399, 13411, 13417, 13421, 13441, 13451, 13457, 13463, 13469, 13477, 13487, 13499, 13513, 13523, 13537, 13553, 13567, 13577, 13591, 13597, 13613, 13619, 13627, 13633, 13649, 13669, 13679, 13681, 13687, 13691, 13693, 13697, 13709, 13711, 13721, 13723, 13729, 13751, 13757, 13759, 13763, 13781, 13789, 13799, 13807, 13829, 13831, 13841, 13859, 13873, 13877, 13879, 13883, 13901, 13903, 13907, 13913, 13921, 13931, 13933, 13963, 13967, 13997, 13999.
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 ā14000 ā 118.3 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 105 primes between 13001 and 14,000, with a total of 1,417,399.
- 3
The biggest gap between neighbouring primes in this range is 30, after 13063 (the next prime is 13093). There are 15 twin prime pairs (primes 2 apart), the first ones (13001, 13003), (13007, 13009), (13217, 13219), (13337, 13339), (13397, 13399), (13679, 13681), (13691, 13693), (13709, 13711).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 13,001 to 14,000 | 105 | 10.5% |
Questions
How many prime numbers are there between 13001 and 14,000?
105.
What is the biggest prime number below 14,000?
13999.
What is the first prime number after 13000?
13001.