lark said:
I have seen that too , but why a design so close to the
Boeing CX-HLS proposal with the number 757 that was again used later ..
This should come as no surprise, since it's consistent with the way Boeing has always used these commercial designations. The company had a license whereby all commercial names following the 7*7 form were theirs by right. That left really only 10 possible aircraft types: 707, 717, 727, 737, 747, 757, 767, 777, 787, 797 (all of which have been now used except for the last one).
At various times in the company's history, projects reached an advanced stage that seemed to justify the release of one of these numbers... However, when the program didn't materialize, Boeing was left with the choice or either jumping to the next number (and thus be short of designations pretty soon), or re-use the unused ones. If you browse through photos of the many designs saved in desktop form at Boeing, you can see this very easily. A more recent example was the reuse of "717" for the former DC-9 line, as that number had not been advertised and very few people would remember it was actually the designation of the KC-135/C-135 series! (not to mention the fact that it was more clever to have all the 7*7 designations applied to the commercial line of products).
At some point during the 1970s, someone must have cleverly remarked how risky it was to start using a designation for an aircraft that hadn't reached production, and those clever figure-letter-figure designations came about: 7X7, 7J7, 7N7.
On a side note, the very same reuse of designations for totally different projects also happened at Douglas, with designations from DC-4 to DC-10 being applied at various moments to projects of sometimes completely different size and form!