Problems & Puzzles: Puzzles

Puzzle 711 Composites with the exactly the same digits than its prime factors The smallest composite that has the same digits that its prime factors is 1255 because: 1225 = 5*251 As a matter of fact there are many examples of biprimes. What is the smallest example of a composite with K prime factors for K=2, 3, 4,.... Here are my findings for K=2, 3, & 4 K Composite Prime factors 2 1255 5, 251 3 163797 3, 71, 769 4 38793587 7, 73, 89, 853 Q. Send your smallest example for K>4.

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Giovanni Resta and Jeff Heleen told me that this puzzle is a repetition of my old  Puzzle 210.  On top of that Jeff and Vicente Felipe Izquierdo wrote that "there is an even smaller solution for K = 4, 11937639 = 3 * 7 * 61 * 9319.". Sorry for this oblivion & mistake.

From Puzzle 210, the results are:

n	Composite	Factorization
2	1255	5*251
3	163797	3*71*769
4	11937639	3*7*61*9319
5	1037715385	5*7*7*83*51031
6	117295838975	5*5*7*89*821*9173
7	11099654778737	7*7*7*7*89*541*96013
8	1091778783077899	7*7*7*7*7*809*8191*9803
9	1023976197718878397	7*7*7*7*61*89*971*983*82301

 

As you will see, no new results were obtained in this second chance.

The new contributions came from Emmanuel Vantieghem, Vicente Felipe Izquierdo and Gérald deGroote.

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Emmanuel wrote:

K Composite           Prime factors

2 1255                     5, 251
3 163797                  3, 71, 769
4 11937639               3, 7, 61, 9319
5 1037715385            5, 7, 7, 83, 51031
6 117295838975        5, 5, 7, 89, 821, 9173
7 115937180777915   5, 7, 7, 7, 811, 9103, 9157 (not minimal, CR)

For  K > 5, I'm not 100% sure that I got the smallest composites.

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Vicente wrote:

k=4,       11937639,   Factors 3,7,61,9319
k=5,   1283777635,   Factors 5,7,61,73,8237 (not minimal, CR)

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Gérald wrote:

for k=5     composite=1370873497     Prime factors=7,43,73,89,701  (not minimal, CR)

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