Industrial-grade prime
Industrial-grade primes (the term is apparently due to
primality has not been certified (i.e. rigorously proven), but they have undergone probable prime tests such as the Miller–Rabin primality test, which has a positive, but negligible, failure rate, or the Baillie–PSW primality test
, which no composites are known to pass.
Industrial-grade primes are sometimes used instead of certified primes in
prime 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 a failure 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.
References
- Prime Pages.
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