Additive Prime Numbers: Is There Anything Known About them?

  • Thread starter Mooky
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Main Question or Discussion Point

A positive integer is called an additive prime number if it is prime and the sum of its digits is also prime. For example, 11 and 83 are additive prime numbers. OEIS gives the sequence of additive primes the number http://oeis.org/A046704" [Broken] for that info).

I've done many Google and MathSciNet searches and could find nothing whatsoever about these numbers. Are there infinitely many of them? What is their density within the primes? There are many questions that could be asked about these, but it appears no one cares. Why is that? Does anyone know anything at all about additive primes, or can offer a link to someone who does?

Thank you,
Mooky
 
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  • #2
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The main reason why few people are interested in additive primes is that the property is not preserved under a change of base ( e.g. decimal to binary). Whether there are infinitely many of them is an open problem.
 
  • #3
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Thank you, Eynstone. I've never thought of that. However, I didn't know that number theorists care much about change of bases when it comes to prime numbers.

There is a http://www.sciencedaily.com/releases/2010/05/100512172533.htm" that proves that the sum of digits of primes is evenly distributed (between odd and even, that is). That propery doesn't carry across bases, either. For example, 13 and 17 have the same digit sum parity in decimal, but 13=11012 (parity 1) whereas 17=100012 (parity 0).
 
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