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Mini-Challenge #4: Palindromic Primes

How many palindromic primes have exactly 5 digits?
How many have exactly 2014 digits?


For a method for finding the prime numbers, see tutorial #3.
If you think you've solved it, or if you're stuck, email pi3challenge@sheffield.ac.uk or tweet to @pi3challenge


What is a palindromic prime?

A palindrome is a word or phrase which is the same when read backwards as forwards. For example, "madam" or "racecar", or "A man, a plan, a canal: Panama" (once spaces and punctuation are removed, and ignoring capitalisation).

A palindromic number is a number that remains the same when its digits are reversed. For example, 1953591. A palindromic prime is a palindromic number which is also a prime number. For example, 757.