About: Largest known squarefree semiprime   Sponge Permalink

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The RSA cryptosystem uses squarefree semiprime moduli. The largest known squarefree (or discrete) semiprime is equal to \((2^{57,885,161} − 1)(2^{74,207,281} − 1) \approx 1.74785212759885802375 imes 10^{39,763,787}\); the factors are the two largest known primes. It should be noted that, because of how sparse the known extremely large primes are, factoring a semiprime this big would be very easy and using it would not guarantee security.

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  • Largest known squarefree semiprime
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  • The RSA cryptosystem uses squarefree semiprime moduli. The largest known squarefree (or discrete) semiprime is equal to \((2^{57,885,161} − 1)(2^{74,207,281} − 1) \approx 1.74785212759885802375 imes 10^{39,763,787}\); the factors are the two largest known primes. It should be noted that, because of how sparse the known extremely large primes are, factoring a semiprime this big would be very easy and using it would not guarantee security.
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abstract
  • The RSA cryptosystem uses squarefree semiprime moduli. The largest known squarefree (or discrete) semiprime is equal to \((2^{57,885,161} − 1)(2^{74,207,281} − 1) \approx 1.74785212759885802375 imes 10^{39,763,787}\); the factors are the two largest known primes. It should be noted that, because of how sparse the known extremely large primes are, factoring a semiprime this big would be very easy and using it would not guarantee security.
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