Prime numbers between 99001 and 100,000
There are 87 prime numbers between 99001 and 100,000: 99013, 99017, 99023, 99041, 99053, 99079, 99083, 99089, 99103, 99109, 99119, 99131, 99133, 99137, 99139, 99149, 99173, 99181, 99191, 99223, 99233, 99241, 99251, 99257, 99259, 99277, 99289, 99317, 99347, 99349, 99367, 99371, 99377, 99391, 99397, 99401, 99409, 99431, 99439, 99469, 99487, 99497, 99523, 99527, 99529, 99551, 99559, 99563, 99571, 99577, 99581, 99607, 99611, 99623, 99643, 99661, 99667, 99679, 99689, 99707, 99709, 99713, 99719, 99721, 99733, 99761, 99767, 99787, 99793, 99809, 99817, 99823, 99829, 99833, 99839, 99859, 99871, 99877, 99881, 99901, 99907, 99923, 99929, 99961, 99971, 99989, 99991.
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 ā100000 ā 316.2 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 87 primes between 99001 and 100,000, with a total of 8,656,623.
- 3
The biggest gap between neighbouring primes in this range is 32, after 99191 (the next prime is 99223). There are 8 twin prime pairs (primes 2 apart): (99131, 99133), (99137, 99139), (99257, 99259), (99347, 99349), (99527, 99529), (99707, 99709), (99719, 99721), (99989, 99991).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 99,001 to 100,000 | 87 | 8.7% |
Questions
How many prime numbers are there between 99001 and 100,000?
87.
What is the biggest prime number below 100,000?
99991.
What is the first prime number after 99000?
99013.