Posted June 18, 200817 yr This one is tougher... I believe each integer can be represented in a way so thati = p1^e1 * p2^e2* p3^e3... * pn^enwhere i is the given integer, p is a set of unique prime numbers, and e is the exponent.For example:1 = 2^02 = 2^13 = 3^14 = 2^25 = 5^16 = 2^1 * 3^17 = 7^18 = 2^39 = 3 ^ 2...96 = 2^5 * 3^1...160 = 2^5 * 5^1...115200 = 2^9 * 3^2 * 5^2Ready?Set! Go!
June 18, 200817 yr Author 10 = 2^1 * 5^111 = 11^112 = 2^2 * 3^113 = 13^114 = 2^1 * 7^115 = 3^1 * 5^116 = 2^417 = 17^118 = 2^1 * 3^219 = 19^120 = 2^2 * 5^121 = 3^1 * 7^122 = 2^1 * 11^123 = 23^124 = 2^3 * 3^125 = 5^226 = 2^1 * 13^127 = 3^328 = 2^2 * 7^129 = 29^130 = 2^1 * 3^1 * 5^1
June 18, 200817 yr Author You love it!!!35 = 5^1 * 7^136 = 2^2 * 3^237 = PRIME!38 = 2^1 * 9^139 = 3^1 * 13*140 = 2^3 * 5^1PS. 32 = 2^5
June 18, 200817 yr Author 41 = PRIME!42 = 2^1 * 3^1 * 7^143 = PRIME!44 = 2^2 * 11^145 = 3^2 * 5^146 = 2^1 * 23^147 = PRIME!48 = 2^4 * 3^149 = 7^250 = 2^1 * 5^2
June 18, 200817 yr Author Keep up with me folks! 51 = 3^1 * 17^1 52 = 2^2 * 13^1 53 = PRIME! 54 = 2^1 * 3^3 55 = 5^1 * 11^1 56 = 2^3 * 7^1 57 = 3^1 * 19^1 58 = 2^1 * 29^1 59 = PRIME! 60 = 2^2 * 3^1 * 5^1
June 20, 200817 yr Author 31 = 31^132 = 2^4 33 = 11^1* 3^1 34 = 17^1*2^1 This is too complicated for me No no no... this is just a nerdy way to do factor trees! 60 = 2 * 2 * 5 *3 since 2 * 2 = 2 ^2 and n^1 = n we can write it like this 60 = 2^2 * 3^1 * 5^1 also... since n^0 = 1 we can throw in more useless numbers to make ourselves look smarter 60 = 2^2 * 3^1 * 5^1 * 7^0 * 11^0 * 13^0
June 21, 200817 yr 61 = PRIME!62 = 2^1 * 31^163 = 3^2 * 7^164 = 2^2 * 2^1 * 2^2^265 = 13^1 * 5^166 = 3^1 * 11^1 * 2^167 = PRIME68 = 17^1 * 2^269 = 3^1 * 23^170 = 7^1 * 5^1 * 2^1
June 24, 200817 yr 71 = PRIME72 = 2^1 * 3^1 * 2^1 * 3^1 *2^173 = PRIME74 = 37^1 * 2^175 = 5^1 * 3^1 * 5^176 = 2^1 * 19^1 * 2^177 = 11^1 * 7^178 = 39^1 * 2^179 = PRIME80 = 2^1 * 2^2 * 2^1 * 5^1
June 24, 200817 yr 81=3^482=2^1*41^!83 - prime84= 2^2*3^1*7^!85=5^1*17^186=2^1*43^187=3^1*29^188=11^1*2^3
June 26, 200817 yr 89 = PRIME90 = 3^2 * 5^1 *2^191 = 7^1 * 13^192 = 23^1 * 2^293 = 3^1 * 31^194 = 2^1 * 47^195 = 5^1 * 19^196 = 4^2 * 2^1 * 3^197 = PRIME98 = 2^1 *49^1
July 6, 200817 yr 99 = 11^1 * 3^2100 = 5^2 * 2^2101 = Prime102 = 17^1 * 3^1 *2^1103 = Prime104 = 13^1 * 2^3105 = 5^1 * 7^1 * 3^1106 = 53^1 * 2^1107 = Prime
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