Prime numbers between 48001 and 49,000
There are 89 prime numbers between 48001 and 49,000: 48017, 48023, 48029, 48049, 48073, 48079, 48091, 48109, 48119, 48121, 48131, 48157, 48163, 48179, 48187, 48193, 48197, 48221, 48239, 48247, 48259, 48271, 48281, 48299, 48311, 48313, 48337, 48341, 48353, 48371, 48383, 48397, 48407, 48409, 48413, 48437, 48449, 48463, 48473, 48479, 48481, 48487, 48491, 48497, 48523, 48527, 48533, 48539, 48541, 48563, 48571, 48589, 48593, 48611, 48619, 48623, 48647, 48649, 48661, 48673, 48677, 48679, 48731, 48733, 48751, 48757, 48761, 48767, 48779, 48781, 48787, 48799, 48809, 48817, 48821, 48823, 48847, 48857, 48859, 48869, 48871, 48883, 48889, 48907, 48947, 48953, 48973, 48989, 48991.
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 ā49000 ā 221.4 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 89 primes between 48001 and 49,000, with a total of 4,317,595.
- 3
The biggest gap between neighbouring primes in this range is 52, after 48679 (the next prime is 48731). There are 13 twin prime pairs (primes 2 apart), the first ones (48119, 48121), (48311, 48313), (48407, 48409), (48479, 48481), (48539, 48541), (48647, 48649), (48677, 48679), (48731, 48733).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 48,001 to 49,000 | 89 | 8.9% |
Questions
How many prime numbers are there between 48001 and 49,000?
89.
What is the biggest prime number below 49,000?
48991.
What is the first prime number after 48000?
48017.