perplexus.info :: Numbers : Inconsiderable Five-Prime Ratio Illation

Inconsiderable Five-Prime Ratio Illation (Posted on 2022-01-12)

p₁, p₂, p₃, p₄ and p₅ are 5 distinct prime numbers, with p₁< p₂<p₃<p₄<p₅, that satisfy this relationship:

 
 p₁*p₂*p₃*p₄*p₅
------------------- = p_x* p_y 
p₁²+p₂²+p₃²+p₄²+p₅²

where p_x and p_y are distinct prime numberε(p₁,p₂,p₃,p₄,p₅).

Determine the minimum value of p_x* p_y.
What is the next smallest value of p_x* p_y?

Submitted by K Sengupta

Rating: 4.0000 (2 votes)

Solution: (Hide)

The minimum value of p_x*p_y is 57, and the next smallest value of p_x*p_y is 69.
For an explanation, refer to:
(1) The solution submitted by Steven Lord here.
(2) The solution submitted by Charlie here.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
No Subject	K Sengupta	2022-02-18 20:48:05
No Subject	hoadao3493	2022-02-18 09:01:25
computer solution	Charlie	2022-01-13 08:10:38
soln	Steven Lord	2022-01-12 10:38:08

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