MHB Palindromic Primes: Find A from 1000-2000

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The discussion centers on finding a palindromic number A, which is the product of two palindromic primes B and C, within the range of 1000 to 2000. It is clarified that while A must be a palindrome, it cannot be a prime number since it is a product of B and C. B is specified to be a two-digit palindromic prime, while C is a three-digit palindromic prime. The participants engage in resolving the conditions for A, emphasizing the constraints on B and C. The conversation highlights the mathematical properties of palindromic numbers and primes.
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given : A=B$\times $C
with the following characters
(1) A,B,C $\in N$
(2)A is a palindrome
(3)B and C are all palindromic primes
(4) 1000<A<2000
(5) B is a 2-digit number
(6) C is a 3-digit number
find A
 
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Albert:

[sp]If A is the product of B and C how can A be prime?[/sp]
 
greg1313 said:
Albert:

[sp]If A is the product of B and C how can A be prime?[/sp]
sorry! A is a palindrome but not a prime
 
only 2 digit palinodromic prime is B = 11
A < 2000 and is of the form 1aa1
from this and C is palinodrom and prime we have C < 2000/11 and C >=100 hence C = 101 or 131 or 151 or 181
giving A = 1111, 1441, 1661, 1881

so we have following combinations (1111 = 1 1 * 101, 1441 = 11 * 131, 1661 = 11 * 151, 1991 = 11 * 181
 

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