Industrial-grade prime
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Industrial-Grade primes are integers for which primaily has not been certified (i.e. rigorously proven), but have undergone a test such as the Miller-Rabin primality test, which has a positive, but impossibly low, failure rate.
Industrial-grade primes are often used instead of certified primes in algorithms such as RSA encryption, which require the user to generate large prime numbers. Say, for example, that I need to test a number that is 100 digits long for primality. Certifying primality for this number would be extremely difficult, even using modern methods. (Trying to prove primality by simply testing every possible prime factor less than it at a trillion trial divisions per second would take over 100000000000000000000 (10^20) times the age of the universe). However, an industrial-grade prime test can accurately test this number for primality almost instantly within an impossibly low failure rate.
In 1998, the Meganet Corporation claimed to have developed an algorithm capable of solving the 400-year old mathematical problem: how to positively identify a prime number without spending exponential time in dividing the number by all the primes up to its root. The solution was called the T-Sequence and is widely considered to be a case of snake oil.
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