Industrial-grade primes (the term is apparently due toHenri Cohen[1]) areintegers for whichprimality has not been certified (i.e. rigorously proven), but they have undergoneprobable prime tests such as theMiller–Rabin primality test, which has a positive, but negligible, failure rate, or theBaillie–PSW primality test, which no composites are known to pass.
Industrial-grade primes are sometimes used instead of certified primes inalgorithms such asRSA encryption, which require the user to generate largeprime numbers.Certifying the primality of large numbers (over 100 digits for instance) is significantly harder than showing they are industrial-grade primes. The latter can be done almost instantly with afailure rate so low that it is highly unlikely to ever fail in practice. In other words, the number is believed to be prime with very high, but not absolute, confidence.
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