Prime numbers between 25001 and 26,000
There are 98 prime numbers between 25001 and 26,000: 25013, 25031, 25033, 25037, 25057, 25073, 25087, 25097, 25111, 25117, 25121, 25127, 25147, 25153, 25163, 25169, 25171, 25183, 25189, 25219, 25229, 25237, 25243, 25247, 25253, 25261, 25301, 25303, 25307, 25309, 25321, 25339, 25343, 25349, 25357, 25367, 25373, 25391, 25409, 25411, 25423, 25439, 25447, 25453, 25457, 25463, 25469, 25471, 25523, 25537, 25541, 25561, 25577, 25579, 25583, 25589, 25601, 25603, 25609, 25621, 25633, 25639, 25643, 25657, 25667, 25673, 25679, 25693, 25703, 25717, 25733, 25741, 25747, 25759, 25763, 25771, 25793, 25799, 25801, 25819, 25841, 25847, 25849, 25867, 25873, 25889, 25903, 25913, 25919, 25931, 25933, 25939, 25943, 25951, 25969, 25981, 25997, 25999.
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 ā26000 ā 161.2 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 98 primes between 25001 and 26,000, with a total of 2,500,168.
- 3
The biggest gap between neighbouring primes in this range is 52, after 25471 (the next prime is 25523). There are 12 twin prime pairs (primes 2 apart): (25031, 25033), (25169, 25171), (25301, 25303), (25307, 25309), (25409, 25411), (25469, 25471), (25577, 25579), (25601, 25603), (25799, 25801), (25847, 25849), (25931, 25933), (25997, 25999).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 25,001 to 26,000 | 98 | 9.8% |
Questions
How many prime numbers are there between 25001 and 26,000?
98.
What is the biggest prime number below 26,000?
25999.
What is the first prime number after 25000?
25013.