MHB Palindromic Primes: Find A from 1000-2000

  • Thread starter Thread starter Albert1
  • Start date Start date
  • Tags Tags
    Primes
Click For Summary
SUMMARY

The discussion focuses on identifying palindromic numbers A within the range of 1000 to 2000, defined by the equation A = B × C, where B and C are both palindromic primes. Key constraints include B being a two-digit number and C a three-digit number. It is clarified that while A must be a palindrome, it cannot be a prime number due to its definition as a product of two factors.

PREREQUISITES
  • Understanding of palindromic numbers
  • Knowledge of prime numbers and their properties
  • Familiarity with number theory concepts
  • Basic multiplication and factorization skills
NEXT STEPS
  • Research palindromic prime numbers between 10 and 999
  • Explore algorithms for generating palindromic numbers
  • Study the properties of products of prime numbers
  • Investigate the significance of palindromic numbers in number theory
USEFUL FOR

Mathematicians, number theorists, and students interested in the properties of palindromic and prime numbers, as well as those exploring mathematical puzzles involving products and palindromes.

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
 

Similar threads

A question on palindromic primes
  • · Replies 2 ·
Replies
2
Views
1K
High School Number of palindromes made of n digits
  • · Replies 5 ·
Replies
5
Views
2K
MHB Max 3-Digit Prime Divisor of 2000!/(1000!1000!)
  • · Replies 1 ·
Replies
1
Views
1K
MHB -c5.LCM and Prime Factorization of A,B,C
  • · Replies 3 ·
Replies
3
Views
1K
MHB What is the highest 3 digit prime factor of ${2000 \choose 1000}$?
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Prime Number Powers of Integers and Fermat's Last Theorem
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Proving Goldbach's conjecture by induction (or why it doesn't seem to work)
  • · Replies 10 ·
Replies
10
Views
3K
MHB Apc.1.1.13 what is the prime factorization of 30,030
  • · Replies 3 ·
Replies
3
Views
1K
Undergrad Union of Prime Numbers & Non-Powers of Integers: Usage & Contexts
  • · Replies 1 ·
Replies
1
Views
2K
MHB What is the Value of N in the Equation N + S(N) = 2000?
  • · Replies 3 ·
Replies
3
Views
1K