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One year ago you were in your prime and twelve years ago you were a power of a prime and now your digits are powers of primes so how old are you now?
Wiki User
∙ 14y ago
Digits that are powers of primes are 22 = 4, 23 = 8, and 32 = 9. So, the possible ages now are 44, 48, 49, 84, 88, 89, 94, 98, and 99.
Twelve years ago you were a power of a prime, so subtract 12 from each of the numbers and look at them. Powers of primes include 22=4, 23=8, 24=16, 25=32, 26=64, 32=9, 33=27, 34=81, 52=25, and 72=49.
44-12=32, a power of 2
48-12=36, not a power of a prime
49-12=37, not a power of a prime
84-12=72, not a power of a prime
88-12=76, not a power of a prime
89-12=77, not a power of a prime
94-12=82, not a power of a prime
98-12=86, not a power of a prime
99-12=87, not a power of a prime
So, 44 fits this part of the question.
We could have started with the other part of the question, first. So, if "one year ago you were in your prime" means that it was a Prime number, the power of a prime which was 12 years ago should produce a prime number when 11 is added to it.
4+11=15, not a prime
8+11=19, a prime
16+11=27, not a prime
32+11=43, a prime
64+11=75, not a prime
9+11=20, not a prime
27+11=38, not a prime
81+11=92, not a prime
25+11=36, not a prime
49+11=60, not a prime
So, the possibilities for one year ago are 19 and 43, meaning the current age is either 20 or 44.
The only number that fits the specifications is 44.
Wiki User
∙ 14y ago
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