I've read XOR encryption is very susceptible to crypto analysis attacks where the key length is less than the length of the plaintext. Also XORing multiple keys of lengths divisible by each other does not increase security, eg: XORing the plaintext with a key of length 4 bytes and then XORing the plaintext with a key of 8 bytes is no more secure than simply XORing the plaintext with only an 8 byte key.
But what if I used keys with lengths of prime numbers, and I apply them in the same manner as above, ie one after the other to the plain text?
For example given four keys of lengths 7, 19, 23 and 29 bytes respectively, if I XOR each of these keys one at a time across the plaintext, does this give me an effective key length of 17*19*23*29 = 215441 bytes because these key lengths are all prime?
Would the key still be susceptible to crypto analysis attacks if I had used a plaintext length matching that effective key length (in this example 215441 bytes) ?