Prime numbers between 28001 and 29,000
There are 98 prime numbers between 28001 and 29,000: 28001, 28019, 28027, 28031, 28051, 28057, 28069, 28081, 28087, 28097, 28099, 28109, 28111, 28123, 28151, 28163, 28181, 28183, 28201, 28211, 28219, 28229, 28277, 28279, 28283, 28289, 28297, 28307, 28309, 28319, 28349, 28351, 28387, 28393, 28403, 28409, 28411, 28429, 28433, 28439, 28447, 28463, 28477, 28493, 28499, 28513, 28517, 28537, 28541, 28547, 28549, 28559, 28571, 28573, 28579, 28591, 28597, 28603, 28607, 28619, 28621, 28627, 28631, 28643, 28649, 28657, 28661, 28663, 28669, 28687, 28697, 28703, 28711, 28723, 28729, 28751, 28753, 28759, 28771, 28789, 28793, 28807, 28813, 28817, 28837, 28843, 28859, 28867, 28871, 28879, 28901, 28909, 28921, 28927, 28933, 28949, 28961, 28979.
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 ā29000 ā 170.3 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 98 primes between 28001 and 29,000, with a total of 2,793,506.
- 3
The biggest gap between neighbouring primes in this range is 48, after 28229 (the next prime is 28277). There are 12 twin prime pairs (primes 2 apart): (28097, 28099), (28109, 28111), (28181, 28183), (28277, 28279), (28307, 28309), (28349, 28351), (28409, 28411), (28547, 28549), (28571, 28573), (28619, 28621), (28661, 28663), (28751, 28753).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 28,001 to 29,000 | 98 | 9.8% |
Questions
How many prime numbers are there between 28001 and 29,000?
98.
What is the biggest prime number below 29,000?
28979.
What is the first prime number after 28000?
28001.