Prime numbers between 98001 and 99,000
There are 87 prime numbers between 98001 and 99,000: 98009, 98011, 98017, 98041, 98047, 98057, 98081, 98101, 98123, 98129, 98143, 98179, 98207, 98213, 98221, 98227, 98251, 98257, 98269, 98297, 98299, 98317, 98321, 98323, 98327, 98347, 98369, 98377, 98387, 98389, 98407, 98411, 98419, 98429, 98443, 98453, 98459, 98467, 98473, 98479, 98491, 98507, 98519, 98533, 98543, 98561, 98563, 98573, 98597, 98621, 98627, 98639, 98641, 98663, 98669, 98689, 98711, 98713, 98717, 98729, 98731, 98737, 98773, 98779, 98801, 98807, 98809, 98837, 98849, 98867, 98869, 98873, 98887, 98893, 98897, 98899, 98909, 98911, 98927, 98929, 98939, 98947, 98953, 98963, 98981, 98993, 98999.
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 ā99000 ā 314.6 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 87 primes between 98001 and 99,000, with a total of 8,572,841.
- 3
The biggest gap between neighbouring primes in this range is 36, after 98143 (the next prime is 98179). There are 13 twin prime pairs (primes 2 apart), the first ones (98009, 98011), (98297, 98299), (98321, 98323), (98387, 98389), (98561, 98563), (98639, 98641), (98711, 98713), (98729, 98731).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 98,001 to 99,000 | 87 | 8.7% |
Questions
How many prime numbers are there between 98001 and 99,000?
87.
What is the biggest prime number below 99,000?
98999.
What is the first prime number after 98000?
98009.