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I'm wondering, is there a name for a prime number where all digits are also prime?

Some examples: 37, 53, 3253, 5573, 23753.

I've been calling them 'double primes', but I doubt that's the correct term (if there is any).

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They aren't interesting enough to deserve a name. –  Gerry Myerson May 5 '12 at 13:03
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Uhm -- choosing a decimal representation is a rather arbitrary choice, which makes me think that this is not a very interesting property. –  user20266 May 5 '12 at 13:05
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Here's a link about them at MathWorld, but no specific name for them. –  hardmath May 5 '12 at 13:20
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Why not call them "prime numbers with only prime digits"? –  GEdgar May 5 '12 at 13:21

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From GEdgar so we have an answer:

Why not call them "prime numbers with only prime digits"?

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Chris Caldwell in his Prime Pages calls them "prime-digit primes."

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