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Let p = a_1a_2.. a_n be a prime number.

Definition: p is "Strange" if p remains prime after deletion of any a_i.

Example 1: 731. If you delete 7 => 31 (prime), if you delete 3 => 71 (prime) if you delete 1 => 73 (prime).

Example 2: 3071. If you delete 3 => 71 (prime), if you delete 0 => 371 (prime) if you delete 7 => 301 (prime), if you delete 1 => 307 (prime).

Question: Are there infinitely may strange prime?

Please tell me anything.



locked by François G. Dorais Dec 28 '11 at 15:05

closed as off topic by Suvrit, Franz Lemmermeyer, Igor Rivin, Zev Chonoles, Felipe Voloch Oct 5 '11 at 13:42

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17*43 == 731 is NOT a prime!! – Suvrit Oct 5 '11 at 13:22
This looks like spam to me, because very of the numbers mentioned are prime (they just look primy, but are not!) --- please clarify – Suvrit Oct 5 '11 at 13:25
Even if the numbers were prime, this is more recreational mathematics than research. – Igor Rivin Oct 5 '11 at 13:37

This is Sloane's A051362. I expect it has only finitely many members, but I don't know of a proof.

One of the most popular questions addresses this precise question.

Nice link with impressive answers. – Suvrit Oct 5 '11 at 13:57
I am Pierre. Thanks for answers. It seems only finitely many possibilities for such strange numbers... When I checked in Wikepedia, super-prime is defined to be a prime sitting in prime order position from the beginning. Is it really called super-prime or my denomination "strange prime" should be better? – pierre matsumi Oct 5 '11 at 18:48
@pierre: I agree that "super-prime" isn't a good term for these. If you need to give them a name "strange prime" is fine, but I prefer to describe them than to name them arbitrarily: "Primes which remain prime after deleting any single decimal digit". If you're writing a paper I'd give the set a variable (S or whatever) and use that. – Charles Oct 5 '11 at 19:34

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