Is it Primus day?

Number Theory Level 3

The positive number k k is the product of four different positive prime numbers. If the sum of these four prime numbers is a prime number greater than 20 20 , what is the least possible value for k k ?


The answer is 390.

Shivamani Patil by shivamani patil , 21, India

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2 solutions

Rama Devi
May 16, 2015

The numbers are 2,3,5,13 . therefore their product is 390.

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Ganesh Ayyappan
Dec 4, 2014

all prime nos. are odd except 1 .... 2 is even ....... Now, Sum of 4 odd nos. is always even ....... so among the 4 prime nos., 1 is even (as 3 odd nos. add up to an odd no ..... wen an odd no. is added to even no. ..... it is odd again)

therefore 1 no. is "2".

Now the least prime number below 20 is 23 .... (v r looking for least no. as v want the least possible product)

23 = 2 + sum of 3 odd nos.

Sum of 3 other odd nos. = 21 ....

now working out all possibilities .... (2,3,5,13) to hav a least product of 390 ...... hence the answer

1 Helpful 0 Interesting 0 Brilliant 0 Confused

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