Prime numbers between 72001 and 73,000
There are 90 prime numbers between 72001 and 73,000: 72019, 72031, 72043, 72047, 72053, 72073, 72077, 72089, 72091, 72101, 72103, 72109, 72139, 72161, 72167, 72169, 72173, 72211, 72221, 72223, 72227, 72229, 72251, 72253, 72269, 72271, 72277, 72287, 72307, 72313, 72337, 72341, 72353, 72367, 72379, 72383, 72421, 72431, 72461, 72467, 72469, 72481, 72493, 72497, 72503, 72533, 72547, 72551, 72559, 72577, 72613, 72617, 72623, 72643, 72647, 72649, 72661, 72671, 72673, 72679, 72689, 72701, 72707, 72719, 72727, 72733, 72739, 72763, 72767, 72797, 72817, 72823, 72859, 72869, 72871, 72883, 72889, 72893, 72901, 72907, 72911, 72923, 72931, 72937, 72949, 72953, 72959, 72973, 72977, 72997.
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 ā73000 ā 270.2 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 90 primes between 72001 and 73,000, with a total of 6,526,174.
- 3
The biggest gap between neighbouring primes in this range is 38, after 72173 (the next prime is 72211). There are 11 twin prime pairs (primes 2 apart): (72089, 72091), (72101, 72103), (72167, 72169), (72221, 72223), (72227, 72229), (72251, 72253), (72269, 72271), (72467, 72469), (72647, 72649), (72671, 72673), (72869, 72871).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 72,001 to 73,000 | 90 | 9% |
Questions
How many prime numbers are there between 72001 and 73,000?
90.
What is the biggest prime number below 73,000?
72997.
What is the first prime number after 72000?
72019.