I think 929573 is missing from http://mathworld.wolfram.com/WeaklyPrime.html because 029573 is prime. Warut On Fri, Mar 13, 2009 at 6:42 AM, Andrew Trevorrow <andrew@trevorrow.com> wrote:

Edwin wrote:

...

Even relaxing the adjacency definition to allow 3-->31 and  3-->13, etc, the graph of all primes will not be connected:

If you change any digit of the prime 971767 it becomes composite. ...

Yep, according to http://mathworld.wolfram.com/WeaklyPrime.html such numbers are said to be "weakly" prime.  According to my code, the first 6 such numbers are:

294001 505447 584141 604171 929573 971767

Note that 929573 is missing from the above MathWorld page.

Some more info about prime ladders:

no. of digits:    2        3        4        5        6 longest ladder:   4        7        9       11       13 example:         23      389     2441    88259   440497                 43      383     5441    88289   410497                 47      883     5741    88789   416497                 37      863     5701    88799   416477                         463     3701    82799   416473                         461     3709    12799   416873                         761     3109    12791   406873                                 9109    92791   406883                                 9199    92761   706883                                         99761   705883                                         99721   705833                                                 905833                                                 995833

Rich gave the challenge of turning 1009 into 9973, and Warut found a few 6-number solutions.  A slightly longer solution is needed to turn 1009 into 9227:

1009 1109 7109 7129 7127 9127 9227

Andrew

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