The unrelated topics in money/security were distracting, perhaps hence ended up into Math.SO to be more specific. Chris provided a good answer but with a misunderstanding about the word bank, I initially assumed that people would consider bank with proper security measures but they did not and the tone was lecturing-and-sarcastic. So instead of solving the key mathematical problem they wasted time on trivialities, the hidden mathematical problem stayed unsolved. Then, the user Fixee noticed my intention and suggested me to rephrase the question. People became a bit chaotic after my change, downvoted it, closed it and moved it to Math.SO. I don't know whether it was due to math-phobia or due to something else but many important mathematically-oriented security-biased questions came to Math.SO (they should belong to Security.SO), a rabbit-rabbit problem at the best. You can read them now in the comments between Fixee and me. I haven't had time yet to ask them in Security.SO, firstly work to be done in Math.SO.
In Math.SO, Ross Millikan found the right words for the problem: semi-primes. In this point, security -related answers became off-topic and distracted discussion. I suggested to remove the unrelated comments in the question and some mod did it. Then, I wanted to clean the answers which did not target the problem as I planned initially with a proper bank definition. I left there notices and down-voted but it distracted more the discussion. The unrelated answers stole the attention from the important answers such as by Ross Millikan. I feel sorry for Ross and Fixii because they tried very hard to solve the core problem (or trying), not stuck to the trivial bank-definition-brute-force-attack -issue or boosting themselves with their intelligence. It was unfortunate that the question went through many sites, becoming more confused, but it is in a way understandable because it is related to all of them. The original problem originates from the scheme of my local bank (which I believe is based on semi-primality which I doubted to be a weak security measure).
But what can mods do here? I hope mods will keep topics relevant to the key site-specific-discussion i.e. primality in this case, currently. I tried (and still trying) to be loyal to the key mathematical problems which people smocked in Security.SO to be just math homework. They are not, look here, actually rather advanced. I hope we can continue to investigate deeper the mathematical issue related to this topic. I believe they can be useful after well-formulation also in Security.SO and perhaps even in Money.SO.