You say

 

 "And the 1st candidate to be checked  would be 10 followed by the digits in ascending order i.e. 104689 " to check whether it's prime " bingo " end  of the process."

 

 That's not the end of the process, as 104689 is not prime, it's 13 * 8053. The next step would be 104698, also not prime (2*11*4759), then 104869. Now's the time for bingo. Beforehand one does not know how many permutations one would have to go through. In this case the third permutation actually works.

 

 Also, I was CURIOUS (a good quality, I had thought) to see if in fact the specification in the text actually led to a solution that indeed fit the title, without staking the answer based on assuming that a 6-digit answer actually existed.

 

 Yes, I was remiss in stating "the first 100 meeting the criterion". I should have said "meeting the most significant (to me) of the criteria specified in the text."

 

 I did not imply that the title should embody the whole of the text. I was only again satisfying my curiosity as to how large we could go and still meet a criterion that had been implied by the title yet not mentioned in the text: that there should be no interloping primes. I'm sorry if the extra information I provided offends you.

 

 In response to " The unsolicited appearance of digit 3 (why only 3,- and not 5 and/or 7 ?) is only due to a bug in the program, that did not exclude all prime digits from the "qualifying digits" set." There are a couple of items:

 

 1. The text of the problem doesn't exclude the appearance of primes so long as all the non-primes are present. Yes, it's true the the smallist, which I admit is all you asked for, does in fact not contain any prime digits; but, as I was extending the list, as I had done several times before to other lists without objection, the extension required only the presence of all the non-primes, not the absence of primes.

 

 2. You ask "why only 3 and not 5 or 7?".  Are you saying that there is a lower number than 1043869 that has all the non-primes, but is contaminated by a prime digit? Later on the list there's also 1046897 that does have a 7 to make the number, while containing all the non-prime digits, contain one that's prime--this time 7.