Prime numbers between 16001 and 17,000
There are 98 prime numbers between 16001 and 17,000: 16001, 16007, 16033, 16057, 16061, 16063, 16067, 16069, 16073, 16087, 16091, 16097, 16103, 16111, 16127, 16139, 16141, 16183, 16187, 16189, 16193, 16217, 16223, 16229, 16231, 16249, 16253, 16267, 16273, 16301, 16319, 16333, 16339, 16349, 16361, 16363, 16369, 16381, 16411, 16417, 16421, 16427, 16433, 16447, 16451, 16453, 16477, 16481, 16487, 16493, 16519, 16529, 16547, 16553, 16561, 16567, 16573, 16603, 16607, 16619, 16631, 16633, 16649, 16651, 16657, 16661, 16673, 16691, 16693, 16699, 16703, 16729, 16741, 16747, 16759, 16763, 16787, 16811, 16823, 16829, 16831, 16843, 16871, 16879, 16883, 16889, 16901, 16903, 16921, 16927, 16931, 16937, 16943, 16963, 16979, 16981, 16987, 16993.
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 ā17000 ā 130.4 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 98 primes between 16001 and 17,000, with a total of 1,617,104.
- 3
The biggest gap between neighbouring primes in this range is 42, after 16141 (the next prime is 16183). There are 13 twin prime pairs (primes 2 apart), the first ones (16061, 16063), (16067, 16069), (16139, 16141), (16187, 16189), (16229, 16231), (16361, 16363), (16451, 16453), (16631, 16633).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 16,001 to 17,000 | 98 | 9.8% |
Questions
How many prime numbers are there between 16001 and 17,000?
98.
What is the biggest prime number below 17,000?
16993.
What is the first prime number after 16000?
16001.