[math-fun] Re: Car Talk and prime numbers

[David Wilson]

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.