Prime numbers between 26001 and 27,000
There are 101 prime numbers between 26001 and 27,000: 26003, 26017, 26021, 26029, 26041, 26053, 26083, 26099, 26107, 26111, 26113, 26119, 26141, 26153, 26161, 26171, 26177, 26183, 26189, 26203, 26209, 26227, 26237, 26249, 26251, 26261, 26263, 26267, 26293, 26297, 26309, 26317, 26321, 26339, 26347, 26357, 26371, 26387, 26393, 26399, 26407, 26417, 26423, 26431, 26437, 26449, 26459, 26479, 26489, 26497, 26501, 26513, 26539, 26557, 26561, 26573, 26591, 26597, 26627, 26633, 26641, 26647, 26669, 26681, 26683, 26687, 26693, 26699, 26701, 26711, 26713, 26717, 26723, 26729, 26731, 26737, 26759, 26777, 26783, 26801, 26813, 26821, 26833, 26839, 26849, 26861, 26863, 26879, 26881, 26891, 26893, 26903, 26921, 26927, 26947, 26951, 26953, 26959, 26981, 26987, 26993.
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 ā27000 ā 164.3 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 101 primes between 26001 and 27,000, with a total of 2,677,675.
- 3
The biggest gap between neighbouring primes in this range is 30, after 26053 (the next prime is 26083). There are 11 twin prime pairs (primes 2 apart): (26111, 26113), (26249, 26251), (26261, 26263), (26681, 26683), (26699, 26701), (26711, 26713), (26729, 26731), (26861, 26863), (26879, 26881), (26891, 26893), (26951, 26953).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 26,001 to 27,000 | 101 | 10.1% |
Questions
How many prime numbers are there between 26001 and 27,000?
101.
What is the biggest prime number below 27,000?
26993.
What is the first prime number after 26000?
26003.