How many numbers are there between 1 and 10,000 that have "prime factors" strictly between 30 and 100 only? No prime factors below 30 and above 100 are allowed. Any help would be greatly appreciated. Thank you.
(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, 3139, 3149, 3233, 3239, 3293, 3337, 3397, 3403, 3431, 3481, 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, 5429, 5561, 5609, 5723, 5767, 5893, 5917, 5963, 6059, 6241, 6319, 6497, 6499, 6557, 6887, 6889, 7031, 7081, 7387, 7663, 7921, 8051, 8633, 9409) = 120 such numbers.
ALL these numbers have Prime Factors that fall between 31 and 97. There are 15 Prime Numbers that form the basis of the 120 numbers above as follows:
31 , 37 , 41 , 43 , 47 , 53 , 59 , 61 , 67 , 71 , 73 , 79 , 83 , 89 , 97. And the above 120 numbers range between 31^2 and 97^2, and are calculated as follows:
15(nCr)2 =105 + 15 squares(31^2, 37^2, 41^2.....and so on = 120 numbers.
