Prime numbers between 96001 and 97,000
There are 84 prime numbers between 96001 and 97,000: 96001, 96013, 96017, 96043, 96053, 96059, 96079, 96097, 96137, 96149, 96157, 96167, 96179, 96181, 96199, 96211, 96221, 96223, 96233, 96259, 96263, 96269, 96281, 96289, 96293, 96323, 96329, 96331, 96337, 96353, 96377, 96401, 96419, 96431, 96443, 96451, 96457, 96461, 96469, 96479, 96487, 96493, 96497, 96517, 96527, 96553, 96557, 96581, 96587, 96589, 96601, 96643, 96661, 96667, 96671, 96697, 96703, 96731, 96737, 96739, 96749, 96757, 96763, 96769, 96779, 96787, 96797, 96799, 96821, 96823, 96827, 96847, 96851, 96857, 96893, 96907, 96911, 96931, 96953, 96959, 96973, 96979, 96989, 96997.
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 ā97000 ā 311.4 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 84 primes between 96001 and 97,000, with a total of 8,107,090.
- 3
The biggest gap between neighbouring primes in this range is 42, after 96601 (the next prime is 96643). There are 7 twin prime pairs (primes 2 apart): (96179, 96181), (96221, 96223), (96329, 96331), (96587, 96589), (96737, 96739), (96797, 96799), (96821, 96823).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 96,001 to 97,000 | 84 | 8.4% |
Questions
How many prime numbers are there between 96001 and 97,000?
84.
What is the biggest prime number below 97,000?
96997.
What is the first prime number after 96000?
96001.