Prime numbers between 39001 and 40,000
There are 96 prime numbers between 39001 and 40,000: 39019, 39023, 39041, 39043, 39047, 39079, 39089, 39097, 39103, 39107, 39113, 39119, 39133, 39139, 39157, 39161, 39163, 39181, 39191, 39199, 39209, 39217, 39227, 39229, 39233, 39239, 39241, 39251, 39293, 39301, 39313, 39317, 39323, 39341, 39343, 39359, 39367, 39371, 39373, 39383, 39397, 39409, 39419, 39439, 39443, 39451, 39461, 39499, 39503, 39509, 39511, 39521, 39541, 39551, 39563, 39569, 39581, 39607, 39619, 39623, 39631, 39659, 39667, 39671, 39679, 39703, 39709, 39719, 39727, 39733, 39749, 39761, 39769, 39779, 39791, 39799, 39821, 39827, 39829, 39839, 39841, 39847, 39857, 39863, 39869, 39877, 39883, 39887, 39901, 39929, 39937, 39953, 39971, 39979, 39983, 39989.
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 ā40000 ā 200.0 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 96 primes between 39001 and 40,000, with a total of 3,791,778.
- 3
The biggest gap between neighbouring primes in this range is 42, after 39251 (the next prime is 39293). There are 9 twin prime pairs (primes 2 apart): (39041, 39043), (39161, 39163), (39227, 39229), (39239, 39241), (39341, 39343), (39371, 39373), (39509, 39511), (39827, 39829), (39839, 39841).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 39,001 to 40,000 | 96 | 9.6% |
Questions
How many prime numbers are there between 39001 and 40,000?
96.
What is the biggest prime number below 40,000?
39989.
What is the first prime number after 39000?
39019.