Prime numbers between 67001 and 68,000
There are 99 prime numbers between 67001 and 68,000: 67003, 67021, 67033, 67043, 67049, 67057, 67061, 67073, 67079, 67103, 67121, 67129, 67139, 67141, 67153, 67157, 67169, 67181, 67187, 67189, 67211, 67213, 67217, 67219, 67231, 67247, 67261, 67271, 67273, 67289, 67307, 67339, 67343, 67349, 67369, 67391, 67399, 67409, 67411, 67421, 67427, 67429, 67433, 67447, 67453, 67477, 67481, 67489, 67493, 67499, 67511, 67523, 67531, 67537, 67547, 67559, 67567, 67577, 67579, 67589, 67601, 67607, 67619, 67631, 67651, 67679, 67699, 67709, 67723, 67733, 67741, 67751, 67757, 67759, 67763, 67777, 67783, 67789, 67801, 67807, 67819, 67829, 67843, 67853, 67867, 67883, 67891, 67901, 67927, 67931, 67933, 67939, 67943, 67957, 67961, 67967, 67979, 67987, 67993.
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 ā68000 ā 260.8 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 99 primes between 67001 and 68,000, with a total of 6,683,189.
- 3
The biggest gap between neighbouring primes in this range is 32, after 67307 (the next prime is 67339). There are 10 twin prime pairs (primes 2 apart): (67139, 67141), (67187, 67189), (67211, 67213), (67217, 67219), (67271, 67273), (67409, 67411), (67427, 67429), (67577, 67579), (67757, 67759), (67931, 67933).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 67,001 to 68,000 | 99 | 9.9% |
Questions
How many prime numbers are there between 67001 and 68,000?
99.
What is the biggest prime number below 68,000?
67993.
What is the first prime number after 67000?
67003.