Prime numbers between 90001 and 91,000
There are 89 prime numbers between 90001 and 91,000: 90001, 90007, 90011, 90017, 90019, 90023, 90031, 90053, 90059, 90067, 90071, 90073, 90089, 90107, 90121, 90127, 90149, 90163, 90173, 90187, 90191, 90197, 90199, 90203, 90217, 90227, 90239, 90247, 90263, 90271, 90281, 90289, 90313, 90353, 90359, 90371, 90373, 90379, 90397, 90401, 90403, 90407, 90437, 90439, 90469, 90473, 90481, 90499, 90511, 90523, 90527, 90529, 90533, 90547, 90583, 90599, 90617, 90619, 90631, 90641, 90647, 90659, 90677, 90679, 90697, 90703, 90709, 90731, 90749, 90787, 90793, 90803, 90821, 90823, 90833, 90841, 90847, 90863, 90887, 90901, 90907, 90911, 90917, 90931, 90947, 90971, 90977, 90989, 90997.
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 ā91000 ā 301.7 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 89 primes between 90001 and 91,000, with a total of 8,051,783.
- 3
The biggest gap between neighbouring primes in this range is 40, after 90313 (the next prime is 90353). There are 10 twin prime pairs (primes 2 apart): (90017, 90019), (90071, 90073), (90197, 90199), (90371, 90373), (90401, 90403), (90437, 90439), (90527, 90529), (90617, 90619), (90677, 90679), (90821, 90823).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 90,001 to 91,000 | 89 | 8.9% |
Questions
How many prime numbers are there between 90001 and 91,000?
89.
What is the biggest prime number below 91,000?
90997.
What is the first prime number after 90000?
90001.