Palindrome Prime Time Part 1

Number Theory Level 1

How many 2-digit prime numbers are palindromes?


The answer is 1.

Alex Segesta by Alex Segesta , 20, USA

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5 solutions

Saurabh Mallik
Mar 27, 2014

There is only 1 1 two-digit palindrome = 11 = \boxed{11}

2 Helpful 0 Interesting 0 Brilliant 0 Confused

Can somebody help me find solutions to this question?

Anagram Cracker!!

Anagrams are problems related to shuffled letters which are needed to be arranged and made into perfect meaningful sentences without repeating the letters (letters can be used only once).

Here are some anagrams which you need to crack:

1) tuteauaewribeifslh

2) geaperioitrdspawsagnhabineod

3) enaednenetorfyimrw

Remember to arrange and make a meaningful sentence (one sentence from each group of letters), not single word. If you are able to solve this anagrams please inform me the answers as well as how you found the solutions to the anagrams.

Details and assumptions:

Example:

"My name is Anil" can be written in the form of group of letters as:

meailaysmnni

Saurabh Mallik - 7 years, 2 months ago
Ganesh Kumar
Mar 20, 2014

only 11

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Nick Turtle
Nov 16, 2017

A two-digit palindrome is always divisible by 11 11 . The first digit and second digit must be the same: 10 a + a = 11 a 10a+a=11a where 0 < a < 10 0<a<10 is an integer.

All two-digit palindromes greater than 11 11 cannot be prime as they have 11 11 as a factor. Therefore, there can only be one number that is both a two-digit palindrome and a prime number: 11 11 .

1 Helpful 0 Interesting 1 Brilliant 0 Confused
Daniel Lim
Mar 3, 2014

It has to be a multiple of 11 11 to satisfy the condition But if it is a multiple of 11 11 , it will not be prime, unless it is 11 11 itself

0 Helpful 0 Interesting 0 Brilliant 0 Confused
David Kim
Mar 2, 2014

Only 11 is a palprime. All other palindromes are divisible by 11 itself.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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