I was reading: Is sharing the modulus for multiple RSA key pairs secure?.

My question is: Given a 1024 bit modulus, how many pairs of 512 bit p's and q's are there that would be able to be combined to create a 1024 bit modulus for use in RSA?

Since a 1024 bit modulus has not been factored, I am guessing we don't know, but I wonder if there is an equation?

I thought it would only be one set honestly: one p and one q multiplied together to get n. (Mainly because they only show 1 set in the wikipedia article: https://en.wikipedia.org/wiki/RSA_numbers#RSA-768)

Maybe I don't understand but the side question would be: Given a 1024-bit modulus, how many pairs of e and d could one come up with?

I was reading: Is sharing the modulus for multiple RSA key pairs secure?.

My question is: Given a 1024 bit modulus, how many pairs of 512 bit p's and q's are there that would be able to be combined to create a 1024 bit modulus for use in RSA?

Since a 1024 bit modulus has not been factored, I am guessing we don't know, but I wonder if there is an equation?

I thought it would only be one set honestly: one p and one q multiplied together to get n. (Mainly because they only show 1 set in the wikipedia article: https://en.wikipedia.org/wiki/RSA_numbers#RSA-768)

Maybe I don't understand but the side question would be: Given a 1024-bit modulus, how many pairs of e and d could one come up with?