Prime numbers between 15001 and 16,000
There are 108 prime numbers between 15001 and 16,000: 15013, 15017, 15031, 15053, 15061, 15073, 15077, 15083, 15091, 15101, 15107, 15121, 15131, 15137, 15139, 15149, 15161, 15173, 15187, 15193, 15199, 15217, 15227, 15233, 15241, 15259, 15263, 15269, 15271, 15277, 15287, 15289, 15299, 15307, 15313, 15319, 15329, 15331, 15349, 15359, 15361, 15373, 15377, 15383, 15391, 15401, 15413, 15427, 15439, 15443, 15451, 15461, 15467, 15473, 15493, 15497, 15511, 15527, 15541, 15551, 15559, 15569, 15581, 15583, 15601, 15607, 15619, 15629, 15641, 15643, 15647, 15649, 15661, 15667, 15671, 15679, 15683, 15727, 15731, 15733, 15737, 15739, 15749, 15761, 15767, 15773, 15787, 15791, 15797, 15803, 15809, 15817, 15823, 15859, 15877, 15881, 15887, 15889, 15901, 15907, 15913, 15919, 15923, 15937, 15959, 15971, 15973, 15991.
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 ā16000 ā 126.5 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 108 primes between 15001 and 16,000, with a total of 1,673,536.
- 3
The biggest gap between neighbouring primes in this range is 44, after 15683 (the next prime is 15727). There are 12 twin prime pairs (primes 2 apart): (15137, 15139), (15269, 15271), (15287, 15289), (15329, 15331), (15359, 15361), (15581, 15583), (15641, 15643), (15647, 15649), (15731, 15733), (15737, 15739), (15887, 15889), (15971, 15973).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 15,001 to 16,000 | 108 | 10.8% |
Questions
How many prime numbers are there between 15001 and 16,000?
108.
What is the biggest prime number below 16,000?
15991.
What is the first prime number after 15000?
15013.