Home > Numbers
Unique semiprime number (Posted on 2010-04-17) |
|
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
|
No Rating
|
|
Solution:
|
(Hide)
|
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 = 3³ * 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.)
|
|
Please log in:
Forums (0)
Newest Problems
Random Problem
FAQ |
About This Site
Site Statistics
New Comments (3)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On
Chatterbox:
|