Question from an intelligent (?) layman

I understand that one element of cryptography is to publish a large
number that is the product of two primes. It is believed impossible to
factor that number (call it N). But can't one make a table of products
of pimes and just compare the key with values in the table? For
example take the primes 2, 3, 5, and 7:

N Primes
--- ---------
6 2*3
10 2*5
14 2*7
15 3*5
21 3*7
35 5*7

Now if N =21, one goes to the table and reads off the answer (3*7). Is
this wrong or am I missing something? I will appreciate any comments.

Al Rosenfield
Columbus OH

.

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