Prime numbers between 18001 and 19,000
There are 94 prime numbers between 18001 and 19,000: 18013, 18041, 18043, 18047, 18049, 18059, 18061, 18077, 18089, 18097, 18119, 18121, 18127, 18131, 18133, 18143, 18149, 18169, 18181, 18191, 18199, 18211, 18217, 18223, 18229, 18233, 18251, 18253, 18257, 18269, 18287, 18289, 18301, 18307, 18311, 18313, 18329, 18341, 18353, 18367, 18371, 18379, 18397, 18401, 18413, 18427, 18433, 18439, 18443, 18451, 18457, 18461, 18481, 18493, 18503, 18517, 18521, 18523, 18539, 18541, 18553, 18583, 18587, 18593, 18617, 18637, 18661, 18671, 18679, 18691, 18701, 18713, 18719, 18731, 18743, 18749, 18757, 18773, 18787, 18793, 18797, 18803, 18839, 18859, 18869, 18899, 18911, 18913, 18917, 18919, 18947, 18959, 18973, 18979.
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 ā19000 ā 137.8 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 94 primes between 18001 and 19,000, with a total of 1,735,092.
- 3
The biggest gap between neighbouring primes in this range is 36, after 18803 (the next prime is 18839). There are 12 twin prime pairs (primes 2 apart): (18041, 18043), (18047, 18049), (18059, 18061), (18119, 18121), (18131, 18133), (18251, 18253), (18287, 18289), (18311, 18313), (18521, 18523), (18539, 18541), (18911, 18913), (18917, 18919).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 18,001 to 19,000 | 94 | 9.4% |
Questions
How many prime numbers are there between 18001 and 19,000?
94.
What is the biggest prime number below 19,000?
18979.
What is the first prime number after 18000?
18013.