Prime numbers between 66001 and 67,000
There are 84 prime numbers between 66001 and 67,000: 66029, 66037, 66041, 66047, 66067, 66071, 66083, 66089, 66103, 66107, 66109, 66137, 66161, 66169, 66173, 66179, 66191, 66221, 66239, 66271, 66293, 66301, 66337, 66343, 66347, 66359, 66361, 66373, 66377, 66383, 66403, 66413, 66431, 66449, 66457, 66463, 66467, 66491, 66499, 66509, 66523, 66529, 66533, 66541, 66553, 66569, 66571, 66587, 66593, 66601, 66617, 66629, 66643, 66653, 66683, 66697, 66701, 66713, 66721, 66733, 66739, 66749, 66751, 66763, 66791, 66797, 66809, 66821, 66841, 66851, 66853, 66863, 66877, 66883, 66889, 66919, 66923, 66931, 66943, 66947, 66949, 66959, 66973, 66977.
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 ā67000 ā 258.8 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 84 primes between 66001 and 67,000, with a total of 5,587,768.
- 3
The biggest gap between neighbouring primes in this range is 36, after 66301 (the next prime is 66337). There are 6 twin prime pairs (primes 2 apart): (66107, 66109), (66359, 66361), (66569, 66571), (66749, 66751), (66851, 66853), (66947, 66949).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 66,001 to 67,000 | 84 | 8.4% |
Questions
How many prime numbers are there between 66001 and 67,000?
84.
What is the biggest prime number below 67,000?
66977.
What is the first prime number after 66000?
66029.