Car Talk and prime numbers

[zak seidov]

Also of interest are changable primes: 
which remain prime
when changing its any digit by any digit 0..9.

It seems that all primes are changable(?).
If so each prime can be assigned by chnum (or
whatever):
number of primes which can be get from given one by
changing its digit. 
Just for example, prime 369293 has 13 child primes: 
changing first digit gives one child prime 869293,
changing 2nd digit gives two child primes
309293,329293,
3rd: 360293,362293,365293,366293,368293,
4th: 369793,369893,
5th: 369253,369263,369283
6th: no child;
total 13.
First chnum's for prime(n)'s are 3,3,3,7,9,8,6:
4th prime 11 has 7 childs: 13,17,19,31,41,61,71, hence
a(4)=7,
5th prime 13 has 8 childs: 3, 11,17,19,23,43,53,73,83,
hence a(5)=9,
6th prime 17 has 8 childs: 7, 11,13,19,37,47,67,97,
hence a(6)=8,
7th prime 19 has 8 childs: 11,13,17,29,59,89, hence
a(7)=6, etc.
Zak
--- David Wilson <davidwwilson at comcast.net> wrote:

> I'm sending this to seqfan because I got temporarily
> banned from math-fun a 
> while ago and I'm not sure I ever got reinstated.
> 
> Anyway,
> 
> An interesting side-concept to deletable primes
> would be insertable primes, 
> that is, primes which can be gotten from another
> prime by deleting one of 
> its digits (or, equivalently, primes for it is
> possible to insert a digit, 
> except for a leading 0, yielding a new prime).
> 
> It turns out that almost all primes are insertable,
> the first few 
> non-insertable primes are
> 
> 369293 3823867 5364431 5409259 7904521 8309369
> 9387527 9510341 22038829
> 27195601 28653263 38696543 39091441 39113161
> 43744697 45095839 45937109
> 48296921 48694231 49085093 49106677 50791927
> 53285777 54128309 56618161
> 57640663 58645603 58781551 60157891 60258467
> 60516983 61106401 68151053
> 68890331 69312091 69326321 70765381 71944009
> 73108603 73694611 74360719
> 74633309 76323007 76813987 77249563 79433461
> 79634173 79968059 80898841
> 85731853 85839461 86605319 87598691 87621403
> 90805097 92375831 92949589
> 93717257 94589251 96403057 99169157 101267767
> 
> Except for a leading 0, no matter where you insert
> (including prepend or 
> append) a digit into these primes you obtain a
> composite.
> 
> Non-insertable primes seem to be rather rare. 
> 
> 


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