How is this different from the largest left-truncatable prime: 357686312646216567629137 (Deleting each digit from the left, in turn, yields a prime all the way till you get to 7). --------------- N. J. A. Sloane wrote:

I asked this list on Saturday about deletable primes. Thanks to everyone who replied. But no one answered my specific question about the largest known deletable prime, so I'm adding these two sequences to the OEIS. Maybe someone would like to extend them! (I will also update them with references to various links that people sent me.) Neil

%I A125589 %S A125589 2,13,103,1013,10039 %N A125589 Smallest n-digit base-10 deletable prime. %C A125589 A prime p is a base-b deletable prime if when written in base b it has the property that removing some digit leaves either the empty string or another deletable prime. "Digit" means digit in base b. %C A125589 Deleting a digit cannot leave any leading zeros in the new string. For example, deleting the 2 in 2003 to obtain 003 is not allowed. %Y A125589 Cf. A080608, A096246, A125590. %K A125589 nonn,base,more,new %O A125589 1,1 %A A125589 njas, Jan 07 2007

%I A125590 %S A125590 7,97,997,9973,99929 %N A125590 Largest n-digit base-10 deletable prime. %e A125590 99929 -> 9929 -> 929 -> 29 -> 2. %Y A125590 Cf. A080608, A096246, A125589. %K A125590 nonn,base,more,new %O A125590 1,1 %A A125590 njas, Jan 07 2007

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----- Original Message ----- From: "N. J. A. Sloane" <njas@research.att.com> To: <math-fun@mailman.xmission.com> Cc: <njas@research.att.com> Sent: Monday, January 08, 2007 9:15 AM Subject: [math-fun] Re: Car Talk and prime numbers

I asked this list on Saturday about deletable primes. Thanks to everyone who replied. But no one answered my specific question about the largest known deletable prime, so I'm adding these two sequences to the OEIS. Maybe someone would like to extend them! (I will also update them with references to various links that people sent me.) Neil

A096243 shows that (number of deletable primes with d+1 digits)/(number of deletable primes with d digits) grows fairly steadily with increasing d. It is not unreasonable to conjecture that this value approaches 10, just as does (number of primes with d+1 digits)/(number of primes with d digits). In other words, I think it is reasonable to conjecture that the deletable primes are infinite in number. I imagine that a statistical case could be made that most primes are insertable, that is, some digit can be inserted to produce a larger prime. At any rate, I was only able to find 61 non-insertable primes <= 10^8. This means that large deletable primes should be fairly easy to generate, as Phil Carmody demonstrated by generating a (probable?) 68-digit deletable prime in less than a second of computer time. I believe the answer to your specific question about the largest known deleteable prime was the 300-digit prime given at http://primes.utm.edu/curios/page.php?number_id=561&submitter=Jobling I don't know if this number has been proved to be a deleteable prime, but I doubt anyone has bothered to try to find a larger deletable prime. I think the main impediment to finding such primes would be the primality testing.