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