Palindromic Primes: Find A from 1000-2000

  • MHB
  • Thread starter Albert1
  • Start date
  • Tags
    Primes
In summary, a palindromic prime is a number that is both a prime number and a palindrome. To find palindromic primes between a range of numbers, we can use a combination of finding all prime numbers in the range and checking if they are also palindromes. These numbers have significance in number theory and cryptography and can be used in creating secure codes and passwords. There is no known pattern or formula for generating palindromic primes, and the largest known one as of 2021 is 998,001 digits long.
  • #1
Albert1
1,221
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
  • #2
Albert:

[sp]If A is the product of B and C how can A be prime?[/sp]
 
  • #3
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
 
  • #4
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
 

1. What is a palindromic prime?

A palindromic prime is a number that is both a prime number (only divisible by 1 and itself) and a palindrome (reads the same forward and backward).

2. How do you find palindromic primes between a range of numbers?

To find palindromic primes between a range of numbers, we can use a combination of two methods: finding all prime numbers within the range, and checking if those prime numbers are also palindromes.

3. What is the significance of finding palindromic primes?

Finding palindromic primes is important in number theory and cryptography. They can also be used in creating secure codes and passwords.

4. Is there a pattern or formula for generating palindromic primes?

No, there is no known pattern or formula for generating palindromic primes. They can only be found through trial and error or using advanced algorithms.

5. What is the largest known palindromic prime?

The largest known palindromic prime as of 2021 is 998,001 digits long and is equal to (10^999,999-10^499,999-1)^2.

Similar threads

B Number of palindromes made of n digits
    • General Math
Replies
5
Views
2K
MHB -c5.LCM and Prime Factorization of A,B,C
    • General Math
Replies
3
Views
554
A question on palindromic primes
    • General Math
Replies
2
Views
874
A Prime Number Powers of Integers and Fermat's Last Theorem
    • General Math
Replies
1
Views
768
I Union of Prime Numbers & Non-Powers of Integers: Usage & Contexts
    • General Math
Replies
1
Views
1K
MHB Max 3-Digit Prime Divisor of 2000!/(1000!1000!)
    • General Math
Replies
1
Views
921
MHB Apc.1.1.13 what is the prime factorization of 30,030
    • General Math
Replies
3
Views
774
I Arithmetic representation of symbols according to certain rules
    • General Math
2
Replies
35
Views
2K
MHB What is the Value of N in the Equation N + S(N) = 2000?
    • General Math
Replies
3
Views
751
MHB What is the highest 3 digit prime factor of ${2000 \choose 1000}$?
    • General Math
Replies
1
Views
1K

Hot Threads

Recent Insights

Back
Top