質數次方: "P^Q + Q^P = R" and P/Q/R are all "Prime Number" (P,Q)=(2,3) or (3,2)

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tt
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質數次方: "P^Q + Q^P = R" and P/Q/R are all "Prime Number" (P,Q)=(2,3) or (3,2)

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"P^Q + Q^P = R" and P/Q/R are all "Prime Number"


P^Q + Q^P = R 而 P/Q/R 都是質數


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Anser #1:  P=2, Q=3, R=17

e.g. 2^3 + 3^2 = 8 + 9 = 17 (True, Prime Number)



NOT Anser #2:  P=2, Q=5, R=57

e.g. 2^5 + 5^2 = 32 + 25 = 57 = 3*19 (FALSE, NOT Prime)



NOT-Anser #3:  P=2, Q=7 or Q=11  or Q=13, or Q=17

e.g. 2^7 + 7^2 = 177 = 3*59  (FALSE, not prime)

e.g. 2^11 + 11^2 = 2048 + 121 = 2169 = 3*3*441  (FALSE, not prime)

e.g. 2^13 + 13^2 = 8361 = 3*3*929  (FALSE, not prime)

e.g. 2^17 + 17^2 = 3*43787  (FALSE, not prime)

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