A prime number is called 'strange' if either it is a one-digit prime, or if each of the numbers obtained by removing its first digit or its last digit are themselves strange primes. How many strange primes are there?

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A prime number is called 'strange' if either it is a one-digit prime, or if each of the numbers obtained by removing its first digit or its last digit are themselves strange primes. How many strange primes are there?
5 Comments
Phil
17/6/2015 11:32:29 pm
2,3,5,7,23,37,53,73,373,737 (and I think that's the lot)
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Tom
18/6/2015 07:15:56 am
737 isn't a strange prime because it isn't a prime at all, it's 11*67.
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Tom
18/6/2015 07:53:35 am
If a number is a strange prime, then evey substring of its decimal representation is also a strange prime. So if there are no strange primes between 10^n and 10^(n+1)-1 inclusive then there are no strange primes a all greater than (10^n)-1.
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Tom
18/6/2015 01:26:19 pm
Actually it's easier to ignore most of the restrictions on the digits used in the decimal representation of primes greater than 10 oher than that the last digit must be 3 or 7 and just do the recursive build using that and the fact that the string omitting the first digit must be a "strange prime".
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Phil
18/6/2015 06:33:13 pm
My (slightly careless!) approach was: ## Leave a Reply. |
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