The RSA cryptosystem uses squarefree semiprime moduli. As of December 7, 2018, the largest known squarefree (or discrete) semiprime is equal to \((2^{77,232,917} − 1)(2^{82,589,933} − 1) \approx 6.958331 \times 10^{48,111,471}\); it is the product of the two largest known primes, which are Mersenne primes. It should be noted that, because of how sparse these large primes are, factoring a semiprime this big would be very easy and using it would not guarantee security.
Approximations in other notations[]
| Notation | Approximation |
|---|---|
| Arrow notation | \(10\uparrow48111417\) |
| Bowers' Exploding Array Function | \(\{10,48111417\}\) |
| Hyper-E notation | E48111417 |
| Hyperfactorial array notation | \(7471738!\) |
| Scientific notation | \(6.958331 \times 10^{48,111,471}\) |