Prime numbers between 10001 and 11,000
There are 106 prime numbers between 10001 and 11,000: 10007, 10009, 10037, 10039, 10061, 10067, 10069, 10079, 10091, 10093, 10099, 10103, 10111, 10133, 10139, 10141, 10151, 10159, 10163, 10169, 10177, 10181, 10193, 10211, 10223, 10243, 10247, 10253, 10259, 10267, 10271, 10273, 10289, 10301, 10303, 10313, 10321, 10331, 10333, 10337, 10343, 10357, 10369, 10391, 10399, 10427, 10429, 10433, 10453, 10457, 10459, 10463, 10477, 10487, 10499, 10501, 10513, 10529, 10531, 10559, 10567, 10589, 10597, 10601, 10607, 10613, 10627, 10631, 10639, 10651, 10657, 10663, 10667, 10687, 10691, 10709, 10711, 10723, 10729, 10733, 10739, 10753, 10771, 10781, 10789, 10799, 10831, 10837, 10847, 10853, 10859, 10861, 10867, 10883, 10889, 10891, 10903, 10909, 10937, 10939, 10949, 10957, 10973, 10979, 10987, 10993.
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 ā11000 ā 104.9 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 106 primes between 10001 and 11,000, with a total of 1,112,190.
- 3
The biggest gap between neighbouring primes in this range is 32, after 10799 (the next prime is 10831). There are 16 twin prime pairs (primes 2 apart), the first ones (10007, 10009), (10037, 10039), (10067, 10069), (10091, 10093), (10139, 10141), (10271, 10273), (10301, 10303), (10331, 10333).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 10,001 to 11,000 | 106 | 10.6% |
Questions
How many prime numbers are there between 10001 and 11,000?
106.
What is the biggest prime number below 11,000?
10993.
What is the first prime number after 10000?
10007.