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Are there any numbers between 1 & 10000 having prime factors between 30 & 140? no prime factors below 30 and above 140 are allowed. any help will be appreciated

 Feb 9, 2022
 #1
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Not sure if I understand your question ! Do you mean: Are there numbers beween 1 and 10,000 that when we factor them, their prime factors fall between 30 and 140?Examples: 1643 ==31 x 53. 4661==59 x 79. 9379==83 x 113......and so on.

 

If that is what is meant, then of course there are such integers. In fact, there are 218 of them whose prime factors fall between 30 and 140.

 Feb 9, 2022
 #2
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961, 1147, 1271, 1333, 1369, 1457, 1517, 1591, 1643, 1681, 1739, 1763, 1829, 1849, 1891, 1927, 1961, 2021, 2077, 2173, 2183, 2201, 2209, 2257, 2263, 2279, 2419, 2449, 2479, 2491, 2501, 2537, 2573, 2623, 2627, 2701, 2747, 2759, 2773, 2809, 2867, 2881, 2911, 2923, 2993, 3007, 3053, 3071, 3127, 3131, 3139, 3149, 3193, 3233, 3239, 3293, 3337, 3397, 3403, 3431, 3481, 3503, 3551, 3569, 3589, 3599, 3649, 3713, 3721, 3763, 3827, 3869, 3901, 3953, 3977, 4087, 4171, 4183, 4187, 4189, 4307, 4331, 4399, 4453, 4489, 4559, 4661, 4717, 4757, 4819, 4891, 4897, 5041, 5063, 5141, 5183, 5251, 5293, 5329, 5353, 5429, 5561, 5609, 5723, 5767, 5893, 5917, 5963, 6059, 6241, 6319, 6497, 6499, 6557, 6887, 6889, 7031, 7081, 7387, 7663, 7921, 8051, 8633, 8927, 9379, 9409 too lazy to know the rest

 Feb 9, 2022
 #3
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There's 24 prime numbers between 30 & 140,

31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139

 Feb 9, 2022
 #4
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I misread the question and found all the ones between 1 and 1000  (not 10000)

I found 202 of them

The question did not aske how many, it simply ask if any existed.  The obvious answer is yes there are lots.

the smallest one is 31

31 is the smallest between 1 and 10000 that has a prime factor between 30 and 40 and no prime factors more than 140 or less then 30.

 

Here is the table I contructed to find how many there are between 1 and 1000

 

 Feb 10, 2022

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