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Even just storing all 2048-bit RSA moduli, assuming the 10^-10 ratio mentioned above, would take about 2^2015 * 2048/8 ~ 10^609 bytes (10^610 bits) of storage. If we could somehow come up with a way of storing one bit per baryon in the entire observable universe and access all that storage instantaneously, then we would need only a measly about 10^530 universes to do this.

Even just storing all 2048-bit RSA moduli, assuming the 10^-10 ratio mentioned above, would take about 2^2015 * 2048/8 ~ 10^609 bytes (10^610 bits) of storage. If we could somehow come up with a way of storing one bit per baryon in the entire observable universe and access all that storage instantaneously, then we would need only a measly about 10^530 universes to do this.

We conclude that the probability of, over 100 years and assuming that we properly generate ten million keys per day, leading to two keys randomly being generated to have the same modulus thus comes out to about 2^-1966 or 10^-592. The number 2^-1966 can be compared to that by the year 2040, we might just barely be able to count up to 2^138 in ten years. It's a long way up the exponential curve from 2^138 to 2^1966, and we'd still have to actually do something with each counted number (like, say, generate a RSA key).

We conclude that the probability of, over 100 years and assuming that we properly generate ten million keys per day, leading to two keys randomly being generated to have the same modulus thus comes out to about 2^-1966 or 10^-592. The number 2^-1966 can be compared to that by the year 2040, we might just barely be able to count up to 2^138 in ten years. It's a long way up the exponential curve from 2^138 to 2^1966, and we'd still have to actually do something with each counted number (like, say, generate a RSA key).

We conclude that the probability of, over 100 years and assuming that we properly generate ten million keys per day, leading to two keys being generated to have the same modulus thus comes out to about 2^-1966 or 10^-592. The number 2^-1966 can be compared to that by the year 2040, we might just barely be able to count up to 2^138 in ten years. It's a long way up the exponential curve from 2^138 to 2^1966, and we'd still have to actually do something with each counted number (like, say, generate a RSA key).

We conclude that the probability of, over 100 years and assuming that we properly generate ten million keys per day, leading to two keys randomly being generated to have the same modulus thus comes out to about 2^-1966 or 10^-592. The number 2^-1966 can be compared to that by the year 2040, we might just barely be able to count up to 2^138 in ten years. It's a long way up the exponential curve from 2^138 to 2^1966, and we'd still have to actually do something with each counted number (like, say, generate a RSA key).