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Unique semiprime number (Posted on 2010-04-17) Difficulty: 1 of 5
What 3-digit number, a product of two distinct 2-digit primes has its digits (none of them being prime) in strictly ascending order ?

  Submitted by Ady TZIDON    
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Ans: 689 There are six non-prime digits -0, 1,4,6,8,&9.:
:
Zero cannot be a part of a 3 digit number whose digits are in strictly ascending order:
So there are ten combinations of three-digit numbers with digits in ascending order using the 5 digits -1,4,6,8, and 9:
146, 148, 149, 168, 169, 189, 468, 469, 489, 689:
Of these, four are even. :
This leaves:
149, 169, 189, 469, 489, 689:
149 is prime, therefore has no prime divisors.:
169= 13*13 so the two divisors are not distinct:
189 = 3 * 7, cannot form two prime divisors.:
489 = 3 * 163, no two- digit divisors. :
This leaves 689 = 13 * 53 :

Comments: ( You must be logged in to post comments.)
  Subject Author Date
Some Thoughtsre: Solution- a tiny remarkAdy TZIDON2010-04-17 17:05:37
SolutionSolutionhoodat2010-04-17 14:37:10
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