Prime numbers between 97001 and 98,000
There are 82 prime numbers between 97001 and 98,000: 97001, 97003, 97007, 97021, 97039, 97073, 97081, 97103, 97117, 97127, 97151, 97157, 97159, 97169, 97171, 97177, 97187, 97213, 97231, 97241, 97259, 97283, 97301, 97303, 97327, 97367, 97369, 97373, 97379, 97381, 97387, 97397, 97423, 97429, 97441, 97453, 97459, 97463, 97499, 97501, 97511, 97523, 97547, 97549, 97553, 97561, 97571, 97577, 97579, 97583, 97607, 97609, 97613, 97649, 97651, 97673, 97687, 97711, 97729, 97771, 97777, 97787, 97789, 97813, 97829, 97841, 97843, 97847, 97849, 97859, 97861, 97871, 97879, 97883, 97919, 97927, 97931, 97943, 97961, 97967, 97973, 97987.
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 ā98000 ā 313.0 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 82 primes between 97001 and 98,000, with a total of 7,995,812.
- 3
The biggest gap between neighbouring primes in this range is 42, after 97729 (the next prime is 97771). There are 15 twin prime pairs (primes 2 apart), the first ones (97001, 97003), (97157, 97159), (97169, 97171), (97301, 97303), (97367, 97369), (97379, 97381), (97499, 97501), (97547, 97549).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 97,001 to 98,000 | 82 | 8.2% |
Questions
How many prime numbers are there between 97001 and 98,000?
82.
What is the biggest prime number below 98,000?
97987.
What is the first prime number after 97000?
97001.