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The "lucky numbers" can be constructed with this sieve. The red ones are the lucky numbers. As you can see, some are prime. Is the number of lucky primes infinite?

Edit: Apparently this is an open problem, so I won't get a proof. However, I do have a replacement question: Can a lucky prime equal a Mersenne prime for n > 10?

Jimmy360
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    According to Wikipedia, the infinitude of lucky primes is an open problem. http://en.wikipedia.org/wiki/Lucky_number – paw88789 May 29 '15 at 20:35
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    @paw88789 Ah, I suppose that I should delete this then. If someone knew, they won't post it here first. – Jimmy360 May 29 '15 at 20:37

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