MHB Palindromic Primes: Find A from 1000-2000

  • Thread starter Thread starter Albert1
  • Start date Start date
  • Tags Tags
    Primes
AI Thread Summary
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.
Albert1
Messages
1,221
Reaction score
0
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
 
Last edited:
Mathematics news on Phys.org
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
 
Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
Is it possible to arrange six pencils such that each one touches the other five? If so, how? This is an adaption of a Martin Gardner puzzle only I changed it from cigarettes to pencils and left out the clues because PF folks don’t need clues. From the book “My Best Mathematical and Logic Puzzles”. Dover, 1994.
Thread 'Imaginary Pythagoras'
I posted this in the Lame Math thread, but it's got me thinking. Is there any validity to this? Or is it really just a mathematical trick? Naively, I see that i2 + plus 12 does equal zero2. But does this have a meaning? I know one can treat the imaginary number line as just another axis like the reals, but does that mean this does represent a triangle in the complex plane with a hypotenuse of length zero? Ibix offered a rendering of the diagram using what I assume is matrix* notation...
Back
Top