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Are there any numbers that have prime factors between 30 & 140 only? You cannot have a prime factor below 30 and a prime factor higher than 40

 Apr 13, 2022
 #1
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The composite numbers whose prime factors fall between 30 & 140 are 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, 3317, 3337, 3379, 3397, 3403, 3431, 3481, 3503, 3551, 3569, 3589, 3599, 3649, 3713, 3721, 3737, 3763, 3811, 3827, 3869, 3901, 3953, 3977, 4087, 4141, 4171, 4181, 4183, 4187, 4189, 4307, 4331, 4343, 4399, 4453, 4489, 4559, 4661, 4717, 4747, 4757, 4819, 4891, 4897, 5041, 5063, 5141, 5143, 5183, 5251, 5293, 5329, 5353, 5429, 5459, 5461, 5561, 5609, 5671, 5723, 5767, 5893, 5917, 5959, 5963, 6059, 6161, 6241, 6319, 6497, 6499, 6557, 6767, 6887, 6889, 7031, 7171, 7081, 7387, 7373, 7663, 7921, 7979, 8051, 8249, 8383, 8633, 8927, 8989, 9379, 9409, 9563, 9797, 9991, 10001, 10201, 10403, 10609, 11021, 11227, 11449, 11881 and 19321

They ALL have prime factors factored between these prime numbers,

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

 Apr 13, 2022
 #2
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There are 24 prime numbers between 30 and 140 and multiplied together should give you:

 

[24  x  25] / 2 ==300 integers - each with 2 prime factors between 30 and 140.

 Apr 13, 2022
 #3
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There's 218 of them

Guest Apr 15, 2022
 #4
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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, 3317, 3337, 3379, 3397, 3403, 3431, 3481, 3503, 3551, 3569, 3589, 3599, 3649, 3713, 3721, 3737, 3763, 3811, 3827, 3869, 3901, 3937, 3953, 3959, 3977, 4033, 4061, 4087, 4141, 4171, 4181, 4183, 4187, 4189, 4223, 4247, 4307, 4309, 4331, 4343, 4387, 4399, 4429, 4453, 4469, 4489, 4559, 4601, 4633, 4661, 4687, 4699, 4717, 4747, 4757, 4819, 4841, 4847, 4859, 4891, 4897, 5029, 5041, 5063, 5069, 5123, 5141, 5143, 5183, 5207, 5251, 5293, 5311, 5329, 5353, 5371, 5429, 5459, 5461, 5561, 5609, 5617, 5633, 5671, 5699, 5723, 5767, 5777, 5891, 5893, 5917, 5959, 5963, 5969, 5977, 5989, 6059, 6077, 6157, 6161, 6241, 6283, 6313, 6319, 6431, 6439, 6497, 6499, 6527, 6533, 6557, 6649, 6667, 6731, 6767, 6887, 6889, 6893, 6901, 6943, 7031, 7081, 7169, 7171, 7261, 7303, 7313, 7367, 7373, 7387, 7493, 7519, 7571, 7597, 7663, 7729, 7739, 7747, 7811, 7921, 7957, 7979, 7991, 8023, 8051, 8083, 8137, 8201, 8249, 8357, 8383, 8453, 8479, 8509, 8549, 8611, 8633, 8777, 8881, 8927, 8989, 9017, 9047, 9167, 9179, 9271, 9301, 9313, 9379, 9409, 9523, 9563, 9701, 9727, 9797, 9869, 9991) = 233 numbers

They all have prime factors that FALL between 30 & 140

 Apr 18, 2022

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