Math Problem Statement
Can you give me a list of all palindromic primes
Solution
A palindromic prime is a prime number that remains the same when its digits are reversed. Here is a list of the smallest palindromic primes:
List of Palindromic Primes:
- 2
- 3
- 5
- 7
- 11
- 101
- 131
- 151
- 181
- 191
- 313
- 353
- 373
- 383
- 727
- 757
- 787
- 797
- 919
- 929
This pattern continues, with numbers becoming larger and more sparse as the primes grow.
If you want to calculate further, the sequence of palindromic primes is infinite, but their density decreases as numbers grow larger.
Do you want details or have any questions?
Here are five questions related to palindromic primes to expand on the topic:
- How do you determine whether a given number is a palindromic prime?
- What is the difference between palindromic primes and regular palindromes in mathematics?
- Are there any palindromic primes with an even number of digits? Why or why not?
- How can we calculate palindromic primes programmatically for very large numbers?
- What applications or significance do palindromic primes have in mathematics?
Tip: When testing if a number is a palindromic prime, ensure to check primality first, as this reduces
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Math Problem Analysis
Mathematical Concepts
Number Theory
Prime Numbers
Palindromic Numbers
Formulas
Definition of a prime number: A number greater than 1 with no divisors other than 1 and itself
Definition of a palindromic number: A number that reads the same forward and backward
Theorems
Fundamental Theorem of Arithmetic: Every integer greater than 1 is either a prime or can be uniquely factored into primes
Basic properties of palindromic numbers in base 10
Suitable Grade Level
Grades 9-12