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Prime Number with Prime Digits

  1. Feb 19, 2014 #1
    Is there a name for a prime number whose digits are all prime? The first several that I can think of are

    2,3,5,7 and 23, 23 being the first double digit prime whose digits are all prime.
  2. jcsd
  3. Feb 19, 2014 #2


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    Well, I don't think so.
    It ought to be just an artefact of the particular number representation system you use.

    If you let "11" be your base number, rather than 10, your "23" will be written as 21, the latter digit not being prime at all.

    The quality of a number being prime is independent of its particular representation, but you cant expext the same for the digits of two distinct representations of the same number.
  4. Feb 19, 2014 #3
    I know that a prime number doesn't depend on its representation, but number theorists have names for different types of primes i.e. Mersenne primes, Irregular primes, Safe primes, and my personal favorite, Sexy primes. I just wanted to know if there was a name for this particular type of prime. For example, as you probably well know there is a name for numbers like 222. They're called palindromic numbers. Now, 313 is a palindromic number but it is also prime. I know that 313 is prime independently of being a palindromic number. That's just a coincidence. My point is, is there a specific name for primes whose digits are all prime? That's all I'm getting at. This also raises the question, are there an infinite number of palindromic primes? Maybe, for the sake of precision, I should have posed my question this way: In a base 10 number system is there a name for a prime number whose digits are all prime?
  5. Feb 19, 2014 #4


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    Mersenne primes are Mersenne primes in all number systems, and so on.

    Sure, some of dubbed palindromic numbers as being palindromic. But, just because you set a name on something doesn't mean it constitutes anything worthwhile studying (i.e, nobody studies palindromic numbers)

    The reason why palindromic numbers have gotten their name is that the property of palindromy is well known outside maths, so it sort of stuck.

    I would be extremely surprised if anyone has given your types of perfectly definable numbers a particular name (I'm not at all saying your question was vague or anything. It wasn't, your first post was perfectly clear)
  6. Feb 19, 2014 #5
    If you count 1 as not being prime, then numbers of this type can't exist in binary. The larger your base is, the more such numbers can exist in that base, because you have more single digit primes. Example, in Hex, B and D are prime. (Funny, I always thought of them as being "even letters".)

    This sounds like "Happy numbers" which are also base dependent.
  7. Feb 19, 2014 #6
    Then I think I will name them Digital Primes.
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