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# Are there different types of prime numbers?

Yes, there are different types of prime numbers, including the following:

• Mersenne primes—See below for an explanation.
• Twin primes—Primes of the form p and p + 2 (in other words, they differ by two); discovering such a prime involves finding two primes.
• Factoridl/primorialprimes—Primorial primes are of the form n# ± 1; factorial primes are of the form n! ± 1.
• Sophie Germain primes—This is an odd prime p for which 2p + 1 is also a prime. It was named after Sophie Germain (1776–1831), who proved that the first case of Fermat’s last theorem for exponents was divisible by such primes.

Other names for prime numbers are mainly for descriptive purposes. For example, in 1984, mathematician Samuel Yates defined a titanic prime to be any prime with at least one thousand digits. In the past few decades since his definition, there have been over a thousand times more such primes discovered. Yates also coined the term gigantic prime to indicate a prime with at least 10,000 digits. Thanks to advances in computer technology, a great deal of prime number generation has happened in the past decade, including surpassing 10,000 digits into the millions. To date, the largest prime number known was uncovered in 2009—a (Mersenne) prime number with 12,978,189 digits, written shorthand as 2 to the power of 43,112,609, minus 1. As to whether mathematicians will eventually find a one billion digit prime number, often referred to as a bevaprime, is no doubt only a matter of time.

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