Prime numbers between 65001 and 66,000
There are 98 prime numbers between 65001 and 66,000: 65003, 65011, 65027, 65029, 65033, 65053, 65063, 65071, 65089, 65099, 65101, 65111, 65119, 65123, 65129, 65141, 65147, 65167, 65171, 65173, 65179, 65183, 65203, 65213, 65239, 65257, 65267, 65269, 65287, 65293, 65309, 65323, 65327, 65353, 65357, 65371, 65381, 65393, 65407, 65413, 65419, 65423, 65437, 65447, 65449, 65479, 65497, 65519, 65521, 65537, 65539, 65543, 65551, 65557, 65563, 65579, 65581, 65587, 65599, 65609, 65617, 65629, 65633, 65647, 65651, 65657, 65677, 65687, 65699, 65701, 65707, 65713, 65717, 65719, 65729, 65731, 65761, 65777, 65789, 65809, 65827, 65831, 65837, 65839, 65843, 65851, 65867, 65881, 65899, 65921, 65927, 65929, 65951, 65957, 65963, 65981, 65983, 65993.
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 ā66000 ā 256.9 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 98 primes between 65001 and 66,000, with a total of 6,418,650.
- 3
The biggest gap between neighbouring primes in this range is 30, after 65449 (the next prime is 65479). There are 14 twin prime pairs (primes 2 apart), the first ones (65027, 65029), (65099, 65101), (65171, 65173), (65267, 65269), (65447, 65449), (65519, 65521), (65537, 65539), (65579, 65581).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 65,001 to 66,000 | 98 | 9.8% |
Questions
How many prime numbers are there between 65001 and 66,000?
98.
What is the biggest prime number below 66,000?
65993.
What is the first prime number after 65000?
65003.