Prime numbers between 73001 and 74,000
There are 83 prime numbers between 73001 and 74,000: 73009, 73013, 73019, 73037, 73039, 73043, 73061, 73063, 73079, 73091, 73121, 73127, 73133, 73141, 73181, 73189, 73237, 73243, 73259, 73277, 73291, 73303, 73309, 73327, 73331, 73351, 73361, 73363, 73369, 73379, 73387, 73417, 73421, 73433, 73453, 73459, 73471, 73477, 73483, 73517, 73523, 73529, 73547, 73553, 73561, 73571, 73583, 73589, 73597, 73607, 73609, 73613, 73637, 73643, 73651, 73673, 73679, 73681, 73693, 73699, 73709, 73721, 73727, 73751, 73757, 73771, 73783, 73819, 73823, 73847, 73849, 73859, 73867, 73877, 73883, 73897, 73907, 73939, 73943, 73951, 73961, 73973, 73999.
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 ā74000 ā 272.0 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 83 primes between 73001 and 74,000, with a total of 6,101,115.
- 3
The biggest gap between neighbouring primes in this range is 48, after 73189 (the next prime is 73237). There are 6 twin prime pairs (primes 2 apart): (73037, 73039), (73061, 73063), (73361, 73363), (73607, 73609), (73679, 73681), (73847, 73849).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 73,001 to 74,000 | 83 | 8.3% |
Questions
How many prime numbers are there between 73001 and 74,000?
83.
What is the biggest prime number below 74,000?
73999.
What is the first prime number after 73000?
73009.