Prime numbers between 40001 and 41,000
There are 88 prime numbers between 40001 and 41,000: 40009, 40013, 40031, 40037, 40039, 40063, 40087, 40093, 40099, 40111, 40123, 40127, 40129, 40151, 40153, 40163, 40169, 40177, 40189, 40193, 40213, 40231, 40237, 40241, 40253, 40277, 40283, 40289, 40343, 40351, 40357, 40361, 40387, 40423, 40427, 40429, 40433, 40459, 40471, 40483, 40487, 40493, 40499, 40507, 40519, 40529, 40531, 40543, 40559, 40577, 40583, 40591, 40597, 40609, 40627, 40637, 40639, 40693, 40697, 40699, 40709, 40739, 40751, 40759, 40763, 40771, 40787, 40801, 40813, 40819, 40823, 40829, 40841, 40847, 40849, 40853, 40867, 40879, 40883, 40897, 40903, 40927, 40933, 40939, 40949, 40961, 40973, 40993.
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 ā41000 ā 202.5 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 88 primes between 40001 and 41,000, with a total of 3,564,578.
- 3
The biggest gap between neighbouring primes in this range is 54, after 40289 (the next prime is 40343). There are 8 twin prime pairs (primes 2 apart): (40037, 40039), (40127, 40129), (40151, 40153), (40427, 40429), (40529, 40531), (40637, 40639), (40697, 40699), (40847, 40849).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 40,001 to 41,000 | 88 | 8.8% |
Questions
How many prime numbers are there between 40001 and 41,000?
88.
What is the biggest prime number below 41,000?
40993.
What is the first prime number after 40000?
40009.